^ 


'3 


7f^ 


IN  MEMORIAM 
FLORIAN  CAJORI 


Digitized  by  the  Internet  Archive 

in  2007  with  funding  from 

IVIicrosoft  Corporation 


http://www.archive.org/details/arithmeticbypracOOwerrrich 


ARITHMETIC  BY  PRACTICE 


BY 
D.  W.  WERREMEYER 

High  and  Manual  Training  School, 
Ft.  Wayne,  Ind. 


NEW  YOEK 

THE  CENTURY  CO. 

1913 


Copyright,  1913, 

BY 

THE  CENTURY  CO. 


W3S 


PREFACE 


The  aim  in  this  book  is  threefold: 

1.  To  provide  for  the  use  of  pupils  in  the  seventh 
and  eighth  grades  a  great  variety  of  practical  problems 
that  are  full  of  content  and  that  involve  the  carrying- 
through  process  and  continuity  of  thought. 

2.  To  train  pupils  to  solve  problems,  not  by  the 
blind  application  of  rules,  but  by  the  application  of 
common  sense  to  the  conditions  of  the  problem;  and 
also  to  lead  the  pupils  to  appreciate  the  fact  that  the 
essential  operations  of  arithmetic  are  not  many  and 
complex  but  few  and  simple. 

3.  To  train  pupils  to  such  simple  and  orderly  ways 
of  setting  down  their  work  as  will  make  for  clearness 
in  thinking  and  economy  in  figuring. 

Fully  seventy-five  per  cent  of  the  problems  in  this 
text  have  been  tried  out  by  the  author  while  Principal 
of  a  ward  school  The  problems  serve  to  carry  out 
the  aim  set  forth  in  this  preface. 

It  is  hoped  that  this  text  may  also  be  found  helpful 
in  the  Schools  of  Education  of  our  Universities,  and 
in  the  Normal  Schools,  where  it  is  difficult  to  find 
proper  material  for  a  twelve  weeks'  course  in  arith- 
metic. It  has  been  the  author's  experience  that  a 
certain  amount  of  problem  work  is  indispensable  in 
such  classes,  and  he  has  found  the  problems  in  this 
text  very  helpful,  since  continuity  of  thought  is,  as  a 
rule,  a  thing  unheard  of  by  beginning  teachers. 

D.   W.  W. 


ivi306091 


CONTENTS 

Chapter  Page 

I. — Expressions  to  be  simplified 1 

II.  —  Problems  involving  Common  Fractions 10 

III. — Problems  involving  Decimal  Fractions 27 

IV.  —  Problems  in  Applications  op  Percentage 41 

V.  —  Problems  in  Measurement  and  Mensuration 66 


AEITHMETIC  BY   PRACTICE 


CHAPTER  I 
Expressions  to  be  Simplified 

The  problems  in  this  chapter  are  intended  to  illus- 
trate and  to  fix  the  rules  concerning  the  precedence 
of  signs  and  the  symbols  of  aggregation.  These  rules 
are  as  follows:  If  only  plus  and  minus  signs  are  in- 
volved, or  if  only  multiplication  and  division  signs 
are  involved,  the  operations  are  performed  in  the  order 
in  which  they  occur;  e.g.,  8+6— 2  =  14— 2  =  12; 
8  -2+6=6+6  =  12;  24  -8x6=3x6=  18; 
24  X  6  -^  8  =  144  ^  8  =  18. 

If  plus  and  minus  signs  are  used  with  either  the 
multiplication  sign  or  the  division  sign,  or  both,  the 
operations  of  multiplication  and  division  are  always 
performed  in  the  order  in  which  they  occur,  but  they 
always  take  precedence  over  addition  and  subtraction; 
e.g.,     6+18  4-2-24-^-6x3=6+9-12  =  15 

-  12  =  3. 

When  symbols  of  aggregation  are  used,  the  expres- 
sion or  expressions  in  such  symbols  are  always  simpli- 
fied  first;    e.g.,    24  -  [18  +  2  -  (15  -^  5  X  4)]  =  24 

-  [18  +  2  -  12]  =  24  -  [20  -  12]  =  24  -  8  =  16. 
The  principal  symbols  of  aggregation  are  the  paren- 
theses (    ),  the  brackets  [    ],  the  vinculum ,  and 

1 


2  ARITHMETIC  BY  PRACTICE 

the  braces  {  |.  The  innermost  symbol  is  usually- 
removed  first,  then  the  next,  and  so  on,  until  all  are 
removed. 

Furthermore,  the  following  problems  are  intended 
to  serve  as  a  drill  on  the  four  fundamental  operations. 
Many  of  them  are  arranged  so  that  the  different  terms 
in  the  problems  can  be  simpUfied  by  inspection.  This 
will  encourage  the  pupil  to  be  on  the  alert  to  simplify 
expressions  without  the  use  of  pencil  wherever  possible. 
Even  in  the  more  complex  problems  towards  the  end 
of  the  list,  the  pupil  should  avail  himself  of  any  scheme 
or  short-cut  that  will  give  him  a  quick  solution.  If 
these  points  are  kept  in  mind  the  simplifying  of  such 
expressions  will  prove  a  valuable  exercise. 

In  the  simplifying  of  expressions  it  is  recommended 
that  the  carrying-through  process  be  used;  i.e.,  simplify 
the  most  complex  parts  of  the  expression  first,  either 
by  inspection  or  otherwise,  but  always  by  inspection 
if  possible.  Then  write  the  simplified  form  in  the 
place  of  the  more  complex  form.  Any  reasonable 
nimoLber  of  steps  in  the  simplifying  of  the  whole  ex- 
pression may  be  taken.  The  number  of  steps  depends 
upon  the  pupiFs  ability.  The  pupil  should  see  that 
the  different  expressions  in  the  several  steps  employed 
are  all  the  same  in  value;  they  are  merely  different  in 
form,  e.g.,  simplify: 

f  +1-  -i  +il  X  A  -  V-  -f  X  ijxi^. 

Solution: 

I  +1  -I  +ir|:x:^x  fi -5:x:^x#= 


EXPRESSIONS  TO  BE  SIMPLIFIED  3 

2,5        7    ,     1    _    1    _  16+20-21        ,    _  J     _ 
3  +  6  ~  8  +  ^g"      2ir  —  24  ^  ^3^      27  — 

1 i_  ^  825  +40-66  ^  865  -  66  ^  799  . 

^  +^3      2»  1320  1320         1320* 

A     •       •      i-f      4*^  8i   .    9f  of  7i 
Again,  simplify:  gf  X  ^^  -.  g^-^^ 

Solution : 

Jl  Ql  Q2  nf  7i  3  7 

5i  ^  io| ""  6  J<,  of  2|  -  ^'  ^  -r  ^  'i:     ^  ^  -^  ^  ^ 

w  -&-1-  V  ^3"  —  -2.1 
A   117  A  -g-    —    16  0- 

iVote.  —  When  a  factor  occurs  in  a  divisor  an  odd 
number  of  times  it  is  inverted.  If  it  occurs  an  even 
number  of  times  it  is  not  inverted.  The  carrying- 
through  process  has  many  advantages  over  the  method 
of  breaking  up  the  expression  into  several  distinct 
problems,  and  then  operating  with  the  several  results. 

Simplify  the  following  expressions: 

1.  4+4x4-4-^4. 

2.  4  X  6  -  96  -H  24  +  56  H-  4  ^  7  -  24  4-  8  X  2. 

3.  (48  X  6  -^  12  -  10  ^  2)  X  6  -  86  X  2  -^  4. 

4.  384  X  16  ^  24  H-  48  X  480  -^  56. 

5.  1024  ^16-34  X  6  ^  4  +  18  +  28  -7-  2. 

6.  [(416  -  216)  -^  50  X  90  -  1000  h-  4]  ^  11  +  70 

-  40  +  80  -  59. 

7.  46  X  16  H-  54  X  9  H-  36  X  280  ^  24. 

8.  750  ^  25  H-  30  X  6  +  4  X  8  -^  2  +  65  -f-  13  X  9. 

9.  56  +  16  -  24  -5-  3  +  15  X  4  +  6  -  75  -^  15. 
10.   16  X  4  -^  8  -  (75  ^  5  X  4  H-  20)  +  17  X  3  X  2 

-^  34  -  7. 


4  ARITHMETIC  BY  PRACTICE 

11.  108  H-  9  +  20  -  81  X  3  ^  9  +  18  X  5  -  16  -  25. 

12.  65  ^  13  X  9  -  40  -  2  +  27  H-  3  +  16  -H  4. 

13.  17  +  9  H-  3  -  15  ^  5  +  11  -  16  +  45 

H-  (7  X  9  ^  3  +  H). 

14.  (14  X  7  -  50)  -T-  (19  X  4  H-  38  X  6)  +  18  +  9  +  5 

-^  (7  X  7  X  2  -^  14  +  2). 

15.  4  X  18  -^  12  X  9  -  48  +  30  +  9  -  (18 

^2X5). 

16.  59  X  2  -  (17  X  6  -  12)  +  54  -  96  -^  8  +  125  ^  5 

-  115  H-  23. 

17.  3  X  48  ^  24  -  110  ^  22  +  98  -;-  2  -  65  ^  13. 

18.  8  X  4  X  6  ^  (9  X  5  ^  15  X  16)  +  68  ^  17  X  9 

-  25  X  25  -I-  125  -  64  ^  16  -^  2. 

19.  96  -i-  16  X  9  +  72  -  80  +  24  +  36  -  48  +  100 

X  30  ^  (60  ^  15  -  2). 

20.  (16+18  +  19-13)  -^  12  X  8  -  76  ^  4  +  15 

+  18  ^  (86  X  3  H-  43). 

21.  6X7^  14 +5x4x6-8x7^-4-3x9x4 

^2-7x6-^2-9x6-^2-8x4^  16. 

22.  (1024  +  2156  -  1560)  -^  45  +  (3864  -  668)  ^  80 

-  2000  ^  80  +  75  -  270  ^  3. 

23.  384  ^  16  ^  8  X  25  +  9  X  15  -  30  X  4  -  16  X  5 

+  2x7x8-7x16+5x6. 

24.  (15  X  25  -  12  X  16  -  9  X  12)  X  4  -  1200  h-  25 

-  3600  -^  90  -  560  -^  14  +  94  +  6  +  525  h- 105. 

25.  [(320  +  640  -  560)  X  20  -  6750  -  625]  h-  25  X  5 

X  4  H-  20. 

26.  (18  X  7  -  19  X  6  +  8  X  12-108  -^  3-  240h-  16) 

-^  19  X  7  -  63  -^  3. 

27.  96  X  2  -  8  +  56  X  4  -  75  X  3  +  18  X  4  -  17 

X5+15x6-60-25+7x8+9^3. 


EXPRESSIONS  TO  BE  SIMPLIFIED  5 

28.  (78  +  86  -  56  ^  14  +  87  H-  29  -  156  -4-  39  +  102 

-i-  17)  ^  33  X  9  -  8  X  5  +  7  X  8  +  14  X  3  -72 
^  24  -  86  +  56  -  48. 

29.  384  ^  16  X  (420  -^  15  X  3  -^  12)  +  196  h-  4 

-  2160  H-  80. 

30.  960  -  1024  ^  8  X  7  +  800  H-  20  -  128  H-  32 

-  600  -i-  8. 

31.  2860  H-  2  -  3500  ^  5  +  87  ^  29  -  56  h-  7 

-  (625  -=-  25  X  25). 

32.  975  -H  25  X  4  -  650  -h  50  h-  (99  ^  11  +  2). 

33.  1600  ^  40  X  3  +  784  ^  8  -  5600  ^  50  -  48  X  2 

+  91  -^13. 

34.  112  X  4  ^  16  -  140  -i-  7  +  51  ^  17  ^  (187  h-  11 

-  6)  -^  1. 

35.  1845  -^  5  ^  9  +  (1675  -^  25  -  17)  -  1460  -^  4 

H-  73  +  14. 

36.  2240  -V-  20  +  360  -  400  +  136  h-  4  X  3. 

37.  16  X  2  +  24  H-  6  -  12  +  7. 

38.  4  +  7  X  4  -  60  H-  20. 

39.  425  X  13  ^  35  +  6  X  175  -  240  h-  6. 

40.  (107  -  7)  H-  20  X  60  -  25  X  8  +  9. 

41.  108  H-  3  -  576  ^  24  X  9  -h  18  +  70  -  18. 

42.  (176,004  +  114,876)  ^  (328  +  756  +  89). 

43.  (980  +  70  -  75)  ^  450  -  375  +  75  -  125 

X  (45  -  15  +20). 

44.  450  X  65  ^  125  -  80  X  60  +  18  h-  3. 

45.  32  +  288  H-  24  -  6  X  8  +  (24  X  6  -  30). 


46.  19  +  26  -  10  ^  (84  -  60  ^  3  -  59)  +  72  +84  h-  12. 

47.  (iV+l-Dxff  ^-V^X3i. 

48.  (.0875  +  6.24  -  .9  -  .004)  X  8.25. 

49.  (I  +  .375  -  f  +  .675  -  ^^)  ^  .25. 


6  ARITHMETIC  BY  PRACTICE 

50.    16  X  8  H- 4  X  96 -3  X4X  161+8 -7x9^-21. 

52.   78  X  54  -h  27  -  25  X  68  -^  17  +  (24  -  6  X  2 

-  2  X  4). 

54.    f +|-|+i-i+|+i- 


T9    ^  T2¥     •     1^ 

'  •  t   ~  t 
KK       ("2      1     7    _     6  ^    V  36    ^  48      I     3 


66.  .025  +  .0078  -  .03  +  8.96  -  5.0002.    . 

57.  .75  X  2.003  h-  5.06. 

58.  .065  -^  .13  X  200  +  (.625  -  .05  ^  25). 

59.  (.875  + 1  -  .9025  X  .06)  X  (.45  ^  .009  X  750). 

60.  l+f -|+HxA-^'--f  X^^Xii 

61.  i+l-l+i-i+f -l+i-iV 

D^.      4    A  9    A  gf    A  10^2^    -8     •     j-g     •     gg. 

63.  .087  +  .00625  +  3.825  -  .99|  -  I.OOIJ  +  6.00i 

-  3.000^V- 

64.  3f  +  2f  -  4f  +  2|  -  1^%  +  .9251  -  .856^. 

65.  7f  +  2.0075  -  6.9256  +  325^  -  180/^. 

66.  ^+i-i+|-TV+TV-TV 

67.  I  +  I  -  f  +*f  X  fi  ^  I  -  H  X  If  X  M- 

68.  IXfy-^-g-g^-^fX-jT-^-  TT*"  X  |f  -^  yy^. 

69.  24.625  +  8.4  -  12.875  +  .006  +  .0075  -  10.775 

+  52.5  -  37.945. 

70.  6i  +  8f  -  5f  +  lOf  -  151  + 17.875  -  12.625. 

71.  324.62  -  180.75  +  60.005  -  .7875  +  200.005 

-  70.8275. 

72.  87  -^  29  X  14  +  105  H-  21  X  6  -  360  4-  72  h-  5 

X  50  +  78  -^  39  X  11. 

73.  56  X  4  -^  8  +  2  -  125  X  5  -I-  25  +  75  X  4  H-  50 

-64^8-^4- 9. 


EXPRESSIONS  TO  BE  SIMPLIFIED  7 

74.  .075  +  .0825  +  .956  -  .0625  -  .0925  +  .875 

-  .00025  +  .008725. 

75.  7.2  +  6.25  -  8.0095  -  2.975  +  .9925  -  .000675 

+  .0875. 

76.  Mi  +  8.75i  -  4.08f  +  12.9835  -  5.05f  +  6.78rV. 

77.  9.625  -  4.00975  +  2|  -  ItV  +  8.725  -  6f . 

78.  8.625  X  2.07  ^  .25  4-  6.75. 

79.  56.45  H-  5  X  18f  -^  .75. 

80.  .64  -i-  .04  +  8.5  ^  .005  -  1600  X  .75  -  18.25^  25 

+  524  ^  .04. 

81.  (93|  X  8.36  H-  12|)  X  Sf. 

82.  (4.8  X  40  H-  6.4  X  7^)  ^  (9.6  -^  1.6  X  15.5  -f-  3.1 

+  6). 

83.  4672.725  X  480.0075  h-  360.000025. 

84.  36  ^  2.4  +  84  -^  .28  -  99.9  -h  3.33  -  484  -i-  2.2 

+ 1024  -^  6.4. 

85.  (.6875  H-  .25  h-  .5  4-  .05)  h-  (.792  ^  .3  h-  .06  ^  .1). 

86.  3^  +  4|  -  5tV  +  8|  -  4f  +  6J-,  -  2|. 

87.  24^  X  16f  -H  15Jj  4-  21Jf  X  56f  ^  48f . 

««    ^  V  8^  _■■  91  of  7i 
^*-  5i^l0i  •  5Jjof2|' 

on    6.725  ,,  18.225  .    36.045 
o".     .  „„_  X 


4.625      24.075     54.0675 

90.  (2f +fof^  +  i)^4/,V 

91.  96  X  1.12  -  (75  -  1.6  X  2.5)  +  96  X  (5  X  .0108 

+  .3642). 
Q2     (3.71  -  1.908)  X  7.03 

2.2  -  .6 
93.   .081  X  1.2|  -h  .006i  X  .016. 


8  ARITHMETIC  BY  PRACTICE 

A        16  03 

Q4.     It  ^  2il.  y  _2i 

18| 

1 KL        973         4.1   _^  as 

18|  ^  36f  ■  9|  H-  12|  * 
96.    (I41J  X  16|f  ^  24f)  +  (44.25  ^  6.5  X  3). 
97    201  .  181  ^  of  #^  A 
•   721  •  84|''f  H-fofff' 

98.  864  ^  12  -  124  h-  (775  -^  25)  +  54  h-  (61  -  34). 

99.  75  —  3^^  —  TT  ~  i  +  5g. 

100.  l^    I   •  ^  • 

©2  I3    X  2' 

101.  (15  -  10  X  .3)  X  6.192  ^  (7  X  5.4  -  35.048). 

102.  I  ^f off  Xf  +1  -^|off  -4-^3^  -1. 

103.  .75  +  .25  X  3  +  1.4  ^  .7  -  .32  X  4. 

104.  (21 +fof^-i|)^l^^. 

105.  530fj,^2|-4|+3f- 
a  1  V  71 

106.  -1  +  7^  H-^-4^- 

4.75  X  8  +  7.248  h-  120  +  8.56  X  .07  +  .071  X  36., 

(2+1)^(3+1) 
(2-i)  x(4-3f)" 
109.    (f +f-TV)  Xif-lxil+y^^+l-^ff- 

1  1  n       6    V     7      V   2  5    V     3_6_  ^   3  5    ^  _7_2_   _^  _6_9_ 

ml      I     3    j_     5  '7    _J_  7  of   3  0  of  1 4    _     8_  of  ^1  of  i-^i- 

of  -^ 
112.   I  -  iSf  -  |of  f  _  lofi  -ioff  +||offf 

113.  (H  - 1  of  if  of  if)  ^  (I  +  H  of  m  of  il). 


107. 
108. 


EXPRESSIONS  TO  BE  SIMPLIFIED 

11K  225    _^885    V     '^^5      ^  JL2  2  5_ 

11A  1184    >v/    3  7  5  0     ^     4780      _i.     2368 

110.  2525    /^  ¥^¥¥     •    ^IT^^T     •    TT«"Fy- 

117  18    _4^f27    _4_7^f32    _10    _i.2.5 

118.  tV  ~  iV  +  isir  ~  "A  +  tV  ""  tV  +  -bV  "~  iV' 

119.  tVV  X  WV  -  ^%  -  (if  X  If  -^  ii). 

120.  foff  ^A-4-lf  xf-Aof|f  ^T^. 


,  CHAPTER  II 
Problems  Involving  Common  Fractions 

The  problems  in  this  chapter  and  in  the  following 
chapters  are  especially  designed  to  emphasize  con- 
tinuity of  thought.  They  are  made  as  practical  as 
possible,  considering  that  conditions  in  different  locali- 
ties are  different,  and  that  what  is  practical  in  one 
community  may  not  be  practical  in  another  community. 

The  present  chapter  deals  with  problems  that  involve 
fractional  relations,  i.e.,  common  fractions.  The  prob- 
lems are  of  such  a  nature  that  various  phases  of  the 
subject  of  arithmetic  are  involved,  e.g.,  many  of  the 
applications  of  percentage;  but  the  fractional  relation 
is  always  used. 

The  solutions  should  be  made  as  concise  as  possible, 
yet  clear  and  complete.  The  following  solutions  for 
the  problems  under  I  in  this  Chapter  are  suggestive: 

1.    (a)  The  depth  X  the  part  =  the  width. 
150  ft.  X  the  part  =  40  ft. 

•.The  part  =  ^^  =  ,-Vo  =  A- 

(6)  The  width  X  the  part  =  the  depth. 
40  ft.  X  the  part  =  150  ft. 

/.The  part  =  ^f^^  =  VV  =  ¥". 

10 


PROBLEMS  INVOLVING  COMMON  FRACTIONS     11 

60 

2.  The  number  of  square  yards  = — —  =  ^^-2- 

=  6661 .  ^ 

3.  The  number  of  feet  in  perimeter  = 

2  (150  +  40)  =  2  X  190  =  380. 
The  number  of  square  feet  in  the  area  = 
150    X  40  =  6000. 
6000  X  the  part  =  380. 

.-.  The  part  =  e Vw  =  sVo- 

4.  (a)  The  price  paid  per  square  foot  =  $1000  -^ 

6000  =  $i  =  16f  cents. 

3 

(6)  The  price  per  square  yard  =  $^  X^  =  $f  = 

$1.50. 

5.  The  cost  at  14  cents  per  square  yard  = 
$.14  X  ^\^-^-  =  $^F   =$93.33i 

6.  The  number  of  posts  =  ^^-  +  4"  +  H^  +  -|-^  = 

5  +  5  +  19  +  19  =  48. 
Note.  —  It  is  impossible  to  place  all  the  posts  8  feet 
apart.     In  two  cases  two  posts  will  be  only  6  feet  apart. 

7.  The  perimeter  of  the  lot  =  380  ft. 

.-.  The  cost  of  the  fence  =  8  cents  X  380  = 
$30.40. 

8.  The  entire  cost  =  $1000  +  $93.33|  +  $30.40  = 
$1123.73i 

;5!421.40  8 

.-.  The  S.  P.  =  $1123.73^  X  |  =  $^^^^  X5=  $1264.20. 
Solutions  like  these  bring  out  clearly  the  facts  stated 
in  the  problem,  and  the  thing  or  things  required  to  be 
found.  They  are  full  of  content  and  at  the  same  time 
concise.  Moreover  they  serve  as  a  stepping-stone  to 
the  solving  of  problems  in  algebra. 


12  ARITHMETIC  BY  PRACTICE 

.       I 

I  purchased  a  lot  40  feet  wide  and  150  feet  deep  for 
$1000. 

1.  The  width  is  what  part  of  the  depth?  The  depth 
is  what  part  of  the  width? 

2.  How  many  square  yards  in  the  lot? 

3.  The  number  of  feet  in  the  perimeter  is  what  part 
of  the  number  of  square  feet  in  the  area? 

4.  How  much  was  paid  per  square  foot?  How  much 
per  square  yard? 

5.  What  will  it  cost  to  sod  the  lot  at  14  cents  per 
square  yard? 

6.  How  many  posts  will  be  required  to  enclose  the 
lot  by  a  fence,  if  the  posts  are  placed  8  feet  apart? 

7.  How  much  will  the  fence  cost  at  8  cents  per  linear 
foot? 

8.  If  I  make  the  above  improvements  on  the  lot, 
and  then  sell  it  at  |  of  the  entire  cost,  how  much  will 
I  receive? 

II 
The  distance  from  Terre  Haute  to  Brazil  is  16  miles. 

1.  How  long  will  it  take  a  train  to  go  from  Terre 
Haute  to  Brazil  at  the  rate  of  40  miles  per  hour? 

2.  How  long  will  it  take  an  interurban  car,  at  the 
rate  of  22  miles  an  hour? 

3.  How  long  will  it  require  to  drive  the  distance  at 
the  rate  of  6  miles  an  hour? 

4.  How  long  will  it  require  to  go  on  a  bicycle  at  the 
rate  of  5  miles  an  hour? 

5.  In  what  time  can  a  man  walk  the  distance  at  the 
rate  of  2|  miles  in  50  minutes? 


PROBLEMS  INVOLVING  COMMON  FRACTIONS     13 

6.  If  the  wheel  of  a  bicycle  is  28  inches  in  diameter, 
how  many  revolutions  will  it  make  in  traveling  from 
Terre  Haute  to  Brazil?  (Circumference  of  wheel 
equals  diameter  X  3|.) 

7.  How  many  revolutions  does  it  make  a  minute? 

8.  The  man  walks  what  part  as  fast  as  the  train 
travels? 

9.  What  is  the  smallest  number  of  miles  that  may 
be  traveled  in  each  of  the  above  five  ways  in  an  integral 
number  of  hours? 

10.  If  the  distance  from  Brazil  to  Indianapolis  is 
3^  times  the  distance  from  Terre  Haute  to  Brazil, 
what  is  the  distance  from  Terre  Haute  to  Indianapolis? 

11.  How  far  from  Indianapolis  is  a  place  that  is 
4|  times  as  far  west  from  Terre  Haute  as  Indianapolis 
is  east? 

Ill 

A,  B,  C,  and  D  own  a  mill  valued  at  $24,000. 

1.  A  owns  I  of  the  mill,  B  owns  |,  C  owns  |,  and  D 
owns  the  remainder.  What  part  of  the  mill  does  D 
own,  and  what  is  his  part  worth? 

2.  B's  share  is  what  part  of  A's,  C's,  and  D's  shares 
respectively? 

3.  B  and  C  together  own  what  part  of  the  mill? 

4.  If  their  net  profit  for  the  year  was  $4800,  how 
should  it  be  apportioned? 

5.  If  the  mill  was  insured  for  f  of  its  value  at  $1.75 
per  hundred,  how  much  insurance  did  each  pay? 

6.  They  traded  the  mill  for  an  elevator  worth  |  as 
much  as  the  mill.     How  much  additional  did  each  pay? 


14  ARITHMETIC  BY  PRACTICE 

IV 

I  purchased  the  south  ^  of  the  northwest  quarter 
of  a  section  of  land. 

1.  Draw  diagram  to  show  how  many  acres  I  have 
purchased. 

2.  How  much  will  the  posts  cost  at  15  cents  each  to 
enclose  the  tract  of  land  by  a  fence,  if  the  posts  are 
placed  16  feet  apart? 

3.  What  will  the  wire  cost  at  35  cents  per  linear  rod? 

4.  How  much  did  I  pay  per  acre  for  the  land,  if  I 
paid  $6040  for  all  of  it? 

5.  If  I  sell  the  farm  for  $7200,  the  selling  price  will 
be  what  part  of  the  cost? 

6.  The  gain  will  be  what  part  of  the  cost? 


A  man  pays  tax  to  the  amount  of  $152.50. 

1.  He  pays  a  poll  tax  of  $2.50.  The  tax  on  his 
personal  property  and  real  estate  is  :^-^  of  the  assessed 
value.  What  is  the  assessed  valuation  of  his  personal 
property  and  real  estate? 

2.  The  assessed  valuation  is  f  of  the  real  value. 
What  is  the  real  value? 

3.  f  of  the  real  value  is  invested  in  a  farm  which  is 
valued  at  $50  per  acre.     How  many  acres  in  the  farm? 

4.  During  a  certain  year,  ^  of  the  farm  was  sown  in 
wheat,  which  yielded  25  bushels  per  acre  and  was  sold 
at  90  cents  per  bushel.  How  much  was  received  for 
the  wheat? 


PROBLEMS  INVOLVING  COMMON  FRACTIONS     15 

5.  i  of  the  remainder  was  planted  in  corn,  which 
yielded  50  bushels  per  acre  and  was  sold  at  60  cents 
per  bushel.     How  much  did  the  corn  bring? 

6.  I  of  the  remainder  was  sown  in  oats,  which 
yielded  35  bushels  per  acre  and  was  sold  at  25  cents 
per  bushel.     How  much  did  the  oats  bring? 

7.  The  remainder  was  put  in  meadow  which  yielded 
5  tons  per  acre  and  was  sold  for  $9  per  ton.  How 
much  was  received  for  the  hay? 

8.  The  gross  income  from  the  farm  was  what  part 
of  the  value  of  the  farm? 

VI 

John,  Harry,  and  James  together  have  243 
marbles. 

1.  John  has  J  as  many  as  Harry,  and  Harry  |  as 
many  as  James.     How  many  has  each? 

2.  Harry  has  what  part  of  all? 

3.  James'  marbles  are  how  many  times  John's  plus 
Harry's? 

4.  How  many  marbles  must  James  give  to  John  and 
how  many  to  Harry  so  that  all  may  have  an  equal 
number? 

5.  If  the  marbles  be  divided  among  John,  Harry, 
and  James  in  the  ratio  of  7,  9,  and  11,  how  many  will 
each  receive? 

6.  Then  John's  marbles  will  be  what  part  of  Harry's 
plus  James'? 

7.  Each  one  now  has  what  part  as  many  as  he  had 
in  the  first  division? 


16  ARITHMETIC  BY  PRACTICE 

VII 

,f  of  Howard's  marbles  are  |  of  Byron's. 

1.  They  together  have  630  marbles.  How  many 
has  each? 

2.  How  many  marbles  must  Byron  give  Howard 
so  that  Howard's  marbles  will  be  |  more  than  Byron's? 

3.  Frederic  comes  forward  with  210  marbles.  He 
has  what  part  of  all  the  marbles? 

4.  Byron's  marbles  are  what  part  of  Howard's  plus 
Frederic's? 

5.  How  many  marbles  must  Howard  give  to  Byron 
and  to  Frederic,  so  that  all  may  have  equal  numbers? 

6.  Divide  all  the  marbles  in  the  ratio  of  8,  9,  and  11. 

VIII 

Three  boys  have  together  22,344  marbles. 

1.  Divide  them  in  the  ratio  of  3,  4,  and  5. 

2.  Divide  them  in  the  ratio  of  7,  8,  and  9. 

3.  Divide  them  in  the  ratio  of  |,  f ,  and  |. 

4.  Divide  them  in  the  ratio  of  f ,  f ,  and  |. 

5.  I  of  I  of  ^V  of  the  marbles  is  what  part  of  f  of  f| 
of  If  of  the  marbles? 

6.  Give  two  interpretations  of  the  expression  ''f." 

IX 

Mr.  Jones  sold  his  interest  in  a  store  for  $5600. 

1.  He  invested  f  of  the  amount  in  the  S.  W.  J  of 
the  N.  E.  i  of  a  section  of  land.  How  much  did  he 
pay  per  acre? 


PROBLEMS  INVOLVING  COMMON  FRACTIONS     17 

2.  He  invested  |  of  the  remainder  in  cattle  at  $25 
per  head.     How  many  cattle  did  he  buy? 

3.  He  invested  the  remainder  in  two  lots,  paying 
f  as  much  for  one  as  for  the  other.  Required  the  price 
he  paid  for  each  lot. 

4.  The  investment  in  land  is  what  part  of  the  invest- 
ment in  cattle? 

5.  The  investment  in  cattle  is  what  part  of  the 
investment  in  each  lot  respectively? 

6.  He  sold  the  less  expensive  lot  so  as  to  gain  f  of 
the  cost.     How  much  did  he  receive? 

7.  He  sold  the  other  lot  and  lost  I  of  the  cost. 
What  was  the  selling  price? 

8.  Did  he  gain  or  lose  on  the  two  lots  and  how 
much? 

9.  He  sold  the  cattle  at  an  average  gain  of  $5  per 
head.     How  much  did  he  receive? 

10.  The  selling  price  of  all  was  what  part  of  the 
cost  of  all? 

11.  The  average  selling  price  per  cow  was  what  part 
of  the  average  cost  per  cow? 


A  man  purchased  a  herd  of  cattle  for  $1760,  paying 
on  the  average  $22  per  head. 

1.  Required  the  number  of  cattle  purchased. 

2.  The  weight  of  the  cattle  was  32,000  pounds. 
What  was  the  cost  per  pound? 

3.  What  was  the  average  weight  per  head? 

4.  The  cattle  were  placed  in  a  pasture  for  five 


18  ARITHMETIC  BY  PRACTICE 

months,  at  the  end  of  which  time  their  weight  had 
increased  f  of  the  original  weight.  Required  the  weight 
of  the  herd. 

5.  They  were  sold  at  an  advance  in  price  of  20  cents 
per  hundred  pounds.  What  amount  was  received  for 
them? 

6.  The  gain  is  what  fractional  part  of  the  cost? 

7.  How  much  was  gained  by  the  advance  in  price? 

8.  If  they  had  been  sold  for  the  same  price  per 
pound  for  which  they  were  purchased,  the  gain  would 
have  been  what  part  of  the  cost?  Find  this  in  two 
ways. 

XI 

Mr.  Jones  pays  a  tax  of  $177.70  including  a  poll  tax 
of  $2.50. 

1.  What  is  the  assessed  valuation  of  Mr.  Jones'  real 
estate  and  personal  property,  if  the  rate  of  taxation 
is  $2|  per  hundred? 

2.  What  is  the  real  value  of  the  assessable  property, 
if  it  is  assessed  for  f  of  the  real  value? 

3.  If  Mr.  Jones  carries  three  years'  insurance  on 
$8000  worth  of  property  at  the  rate  of  $f  per  hundred, 
what  is  the  premium? 

4.  Mr.  Jones  sold  a  piece  of  property  that  cost  him 
$3600,  at  a  gain  of  |  of  the  cost.  What  was  the  selUng 
price  and  what  was  the  gain? 

5.  A  commission  agent  sold  the  property  for  Mr. 
Jones  and  charged  ^f^  of  what  he  received.  What 
was  his  commission? 


PROBLEMS  INVOLVING  COMMON  FRACTIONS     19 

6.  How  much  would  Mr.  Jones  have  received  if  he 
had  asked  $4500  for  the  property  and  then  sold  it  at 
tV  and  iV  off? 

7.  His  gain  would  have  been  what  part  of  the  cost? 

XII 

In  a  certain  high  school  there  are  enrolled  850 
pupils. 

1.  There  are  f  as  many  boys  as  girls.  How  many 
boys  and  how  many  girls  are  enrolled? 

2.  The  number  of  boys  and  the  number  of  girls  is 
respectively  what  part  of  the  enrollment? 

3.  The  number  of  boys  is  yV  of  how  many  boys? 

4.  The  number  of  girls  is  f  of  ||  of  how  many  girls? 

5.  The  enrollment  in  another  high  school  is  2125. 
This  is  what  part  of  the  enrollment  in  the  first  school? 

6.  The  ratio  of  the  number  of  boys  to  the  number 
of  girls  in  number  5  is  42  :  43.  Required  to  find  the 
number  of  boys  and  the  number  of  girls. 

7.  Divide  1728  in  the  ratio  of  5,  9,  and  13. 


20 


ARITHMETIC  BY  PRACTICE 


XIII 


%  inch 

.9 
1  inch         ^ 

H 

1 

1  inch 

D 

1 

m  inches 

-s 

.9 

;?; 

F 
1 

E 

1.  What  is  the  length  of  Une  AB? 

2.  What  is  the  length  of  line  AJ? 

3.  What  is  the  perimeter  of  the  figure? 

4.  Line  AJ  is  what  part  of  the  perimeter?   What  part 
of  line  AB? 

5.  Line  EF  is  what  part  of  line  HI?  of  line  BC? 

6.  Line  AB  is  what  part  of  a  foot?     Of  a  yard?    Of 
a  rod? 

7.  Line  AJ  is  what  part  of  a  foot?    Of  a  yard? 
Of  a  rod? 

8.  Line  EF  plus  line  HI  is  what  part  of  a  foot? 
Of  a  yard?    Of  a  rod? 


PROBLEMS  INVOLVING  COMMON  FRACTIONS     21 
XIV 

^mUe 


%  mfle 

s— 


s5 


H 


1.  H  is  Frederic's  home  and  S  is  the  school  he 
attends.  How  many  miles  must  he  ride  to  school  on 
his  wheel? 

2.  What  part  of  the  journey  has  he  taken  when  he 
reaches  the  first  corner? 

3.  What  part  of  the  journey  has  he  taken  when  he 
reaches  the  second  corner? 

4.  Where  is  the  halfway  point? 

5.  How  many  rods  from  the  second  corner  to  the 
third  corner?     From  the  third  corner  to  the  school? 

6.  How  many  miles  does  Frederic  ride  per  day  if  he 
goes  home  for  lunch? 

7.  How  many  miles  will  he  ride  during  eight  school 
months,  deducting  three  holidays? 


22 


ARITHMETIC  BY  PRACTICE 


XV 


■s 

160  feet 

1 

20  feet 

o 

■s 

1 

80  feet 

1 

o 

& 

60  feet 


1.  This  figure  is  a  plan  of  a  lot.  What  is  the  perim- 
eter in  rods?    What  is  the  perimeter  in  miles? 

2.  How  many  posts  can  be  set  on  the  boundary  ten 
feet  apart? 

3.  How  many  rods  of  wire  will  be  required  to  enclose 
it  by  a  fence  of  six  wires? 

4.  Find  out  the  cost  of  smooth  wire  for  fencing  and 
determine  the  total  cost  of  the  wire. 

5.  If  the  rectangle  40  feet  by  60  feet  in  the  plan  is 
enclosed  by  a  fence,  how  many  fruit  trees  can  be  planted 
in  the  same,  if  they  are  placed  at  least  3|  feet  from  the 
fence  and  at  least  one  rod  apart? 

6.  If  a  cement  walk  four  feet  wide  is  placed  along 
the  side  160  feet  long,  and  along  the  side  60  feet  long, 
how  many  square  feet  does  the  walk  contain? 

7.  The  area  of  the  walk  is  what  fraction  of  an  acre? 


PROBLEMS  INVOLVING  COMMON  FRACTIONS     23 

XVI 

A  commission  agent  purchased  a  farm  for  Mr.  Rose. 
He  paid  $5600  for  the  farm  and  charged  $80  commission. 

1.  What  was  the  total  cost  of  the  farm  to  Mr.  Rose? 

2.  What  part  of  the  investment  in  the  farm  did  the 
agent  charge  for  his  commission? 

3.  If  the  farm  contained  75  acres,  what  price  did 
the  agent  pay  per  acre? 

4.  The  commission  exceeds  the  cost  per  acre  by  how 
much?  The  cost  per  acre  is  what  part  of  the  com- 
mission? 

5.  Required  the  amount  of  tax  to  be  paid  on  the 
farm  at  the  rate  of  $2.63  per  hundred  dollars,  the  farm 
being  assessed  for  |  of  its  value? 

6.  What  must  be  the  net  income  from  the  farm  to 
yield  ^^^o^  of  the  total  investment? 

7.  f  of  the  cost  of  the  farm  is  f  of  what  sum? 

XVII 

I  purchased  a  lot  60  feet  wide  and  160  feet  deep  for 
$800. 

1.  How  many  square  yards  in  the  area  of  the  lot? 

2.  How  much  did  the  lot  cost  per  front  foot? 

3.  How  much  did  it  cost  per  square  foot?  How 
much  per  square  yard? 

4.  I  built  a  barn  lengthwise  in  one  corner  of  the  lot. 
The  barn  is  60  feet  long  and  40  feet  wide.  The  base 
of  the  barn  covers  what  part  of  the  lot? 

5.  How  many  posts  are  required  to  build  a  fence 


24  ARITHMETIC  BY  PRACTICE 

around  the  remainder  of  the  lot,  if  they  are  placed 
6  feet  apart  as  nearly  as  possible? 

6.  Required  to  find  the  number  of  boards  12  feet 
long  to  build  a  fence  six  boards  high  around  the  lot. 
(The  barn  is  to  serve  as  a  fence.) 

7.  Required  to  find  the  cost  of  these  boards,  if  they 
are  6  inches  wide,  at  $1.75  per  hundred  board  feet? 

8.  The  cost  of  the  fence  is  what  part  of  the  cost  of 
the  lot? 

XVIII 

I  purchased  a  rectangular  plot  of  ground,  containmg 
one  acre,  for  $120. 

1.  If  the  plot  is  8  rods  wide,  how  long  is  it? 

2.  What  was  the  cost  per  square  rod? 

3.  I  planted  the  plot  in  com.  If  the  rows  run  the 
long  way,  how  many  rows  are  there  if  the  rows  are 
2^  feet  apart  and  the  outside  rows  are  one  foot  from 
the  fence? 

4.  Single  grains  are  planted  20  inches  apart  and 
10  inches  from  each  end.  How  many  grains  are 
planted? 

5.  If  on  the  average  each  grain  produces  an  ear  of 
corn,  what  is  the  total  number  of  ears? 

6.  How  many  bushels  have  been  raised,  counting 
80  ears  to  a  bushel? 

7.  How  much  is  the  corn  worth  at  65  cents  per 
bushel? 

8.  Counting  |  of  the  receipts  for  expenses,  what 
part  of  the  investment  of  the  lot  was  realized? 


PROBLEMS  INVOLVING  COMMON  FRACTIONS     25 
XIX 


The  broken  line  A  B  C  D  E  F  represents  a  road. 
A,  B,  C,  D,  and  F  represent  cities. 

1.  How  far  will  a  man  travel  on  his  wheel  to  go 
from  A  to  F? 

2.  How  long  will  it  require  to  travel  this  distance 
at  the  rate  of  2|  miles  in  15  minutes? 

3.  The  distance  from  A  to  B  is  what  part  of  the 
distance  from  A  to  F? 

4.  The  distance  from  B  to  D  is  what  part  of  the 
distance  from  A  to  B? 

5.  If  two  men  leave  A  and  F  respectively  at  the 
same  time  and  travel  at  the  same  rate  toward  each 
other,  where  will  they  meet? 

6.  The  number  of  miles  each  traveled  is  what  part 
of  the  distance  from  C  to  D? 

XX 

A  man's  annual  income  is  $1800. 

1.  I  of  this  income  is  from  a  farm.  What  is  the 
value  of  the  farm,  if  the  income  is  ^  of  the  value? 

2.  I  of  the  income  is  from  an  investment  in  a  mine. 


26  ARITHMETIC  BY  PRACTICE 

This  income  is  ^  of  tiie  investment.     What  is  the 
investment? 

3.  I  of  the  income  is  from  bank  stock.  What  is  the 
investment  in  bank  stock,  if  the  income  is  /^  of  it? 

4.  I  of  the  income  is  rent  for  a  dwelling.  The  in- 
come is  -i^  of  the  value  of  the  dwelling.  What  is  the 
value  of  the  dwelling? 

5.  What  part  of  the  income  is  not  yet  accounted  for? 

6.  The  remaining  income  is  ^V  ^f  the  amount  of 
money  he  has  on  interest.  What  amount  has  he  on 
interest? 

7.  The  total  income  is  what  part  of  the  total  in- 
vestment? 


CHAPTER  III 

Problems  Involving  Decimal  Fractions 

In  the  problems  in  this  chapter  the  notion  of  decimal 
fractions  is  predominant.  In  some  cases  the  pupils 
will  be  required  to  investigate  the  current  prices  of 
certain  articles;  e.g.,  groceries,  as  in  sets  I,  II,  III, 
and  IV. 

Many  of  the  problems  in  this  chapter  are  similar  to 
those  in  Chapter  II,  except  that  decimal  fractions  are 
used  instead  of  common  fractions.  Hence  the  method 
of  procedure  in  solving  the  problems  will  be  the  same. 
The  following  solutions  of  the  problems  in  set  XV  are 
intended  to  be  suggestive: 

1.  The  assessed  valuation  =  $1500  X  .55  =  $825. 
The  no.  of  $100  =  $825  ^  $100  =  8.25. 

.-.  The  tax  =  $2.84  X  8.25  =  $23.43. 

2.  The  amount  for  which  the  machine  is  insured 
=  $1500  X  .75  =  $1125. 

The  no.  of  $100  =  $1125  ^  $100  =  11.25. 
.-.  The  premium  =  $.80  X  11.25  =  $9. 

3.  The  amount  of  depreciation  =  $1500  X  .35  = 
$525. 

.-.  The  value  would  then  be  $1500  -  $525  =$975. 

4.  The  cost  X  the  no.  of  Jiundredths  ^  ^^^^ 

$1500  X  ^^^  '''''  of^  hundredths  ^  ^g^^^ 
27 


28  ARITHMETIC  BY  PRACTICE 

.-.  The  no.  of^hundredths  ^  ^^^^  ^  ^^^^^  ^   g^^ 

/.  The  no.  of  hundredths  =  .60  X  100  =  60. 

5.  The  number  of  acres  purchased  =  $900  -t-  $75 
=  12. 

6.  The  amount  of  rent  per  acre  =  $75  X  .07  =$5.25. 


Using  the  current  market  price  find  the  cost  of: 

1.  1  qt.  of  cranberries;  3  qts.;  1  gal. 

2.  1  pk.  of  apples;  |  pk.;  1  bu. 

3.  I  bu.  of  sweet  potatoes;  |  pk.;  2  bu. 

4.  lib.  of  coffee;  Jib.;  2  lbs. 

5.  Ub.  of  tea;  lib.;  i  lb. 

6.  2  lbs.  of  corn  meal;  5  lbs.;  10  lbs. 

7.  I  doz.  bananas;  IJ  doz. 

8.  2  bars  of  laundry  soap ;  3;  5;  10. 

9.  1  qt.  navy  beans;  2  qts.;  1  pk. 

10.  5  lbs.  of  granulated  sugar;  25  lbs. 

11.  25  lbs.  of  the  best  flour;  100  lbs. 

12.  1|  lbs.  of  beef  steak;  3|  lbs.;  5  lbs. 

II 

Using  the  current  market  price  find  amount  of: 

1.  Starch  to  be  given  for  10c. ;  15c.;  25c. 

2.  English  walnuts,  5c. ;   10c. ;  25c. 

3.  Pepper,  10c. ;  15c.;  20c. 

4.  Rice,  10c. ;  25c.;  50c. 

5.  Granulated  sugar,  25c. ;  50c.;  $1.00. 


PROBLEMS  INVOLVING  DECIMAL  FRACTIONS  2a 

6.  Butter,  15c.;  35c.;  50c. 

7.  Soap,  25c.;  50c.  $1.00. 

8.  Prunes,  25c.;  50c. 

9.  Apricots,  25c.;  50c. 

10.  Chicken,  30c.;  50c.;  $1.00. 

11.  Veal  steak,  25c.;  50c.;  80c. 

12.  Eggs,  15c.;  25c.;  60c. 

Ill 

Compare  the  cost  of: 

1.  Sugar  when  bought  by  the  pound  and  by  the 
25-lb.  sack. 

2.  Toilet  soap,  when  bought  by  the  bar,  and  by  the 
quarter's  worth. 

3.  Laundry  soap,  when  bought  by  the  bar  and  by 
the  quarter's  worth;  by  the  bar  and  by  the  box;  by 
the  quarter's  worth  and  by  the  box. 

4.  Potatoes,  bought  by  the  quarter-peck,  by  the 
peck,  and  by  the  bushel. 

5.  Sweet  potatoes,  bought  as  in  4. 

6.  Canned  goods,  when  bought  by  the  can  and  by 
the  dozen. 

IV 

Make  out  a  bill  for  the  following  order  of  goods, 
using  prevailing  market  prices : 

3  loaves  of  bread;  5  lbs.  of  granulated  sugar;  1  lb. 
butter;  IJ  lbs.  pork  chops;  2  dozen  eggs;  1  lb.  coffee; 
^  lb.  tea  at  60c.;  celery,  10c. ;  1  pt.  oysters;  ^  pk. 
peaches;   1  lb.  crackers. 


30  ARITHMETIC  BY  PRACTICE 

V 

Make  out  a  bill  for  the  following  order  of  goods: 

2|  yds.  of  lace  at  25c.  a  yd.;  3 J  yds.  of  hair  ribbon 
at  35c.  a  yd.;  8  yds.  of  calico  at  8Jc.  a  yd.;  12  yds. 
of  percale  at  15c.  a  yd.;  5  yds.  of  dress  goods  at  12Jc. 
a  yd.;  3  handkerchiefs  at  25c.  each;  7  yds.  of  silk  at 
$1.39  a  yd.;  f  of  a  yd.  of  velvet  ribbon  at  20c.  a  yd. 


VI 

The  following  table  shows  the  deposits  and  number 
of  depositors  for  a  certain  Trust  Company  for  eight 
days: 


Date  Deposits 

October  10 $2,250. . 


No.  of  Depositors 
18 


11 

13 

14 

15 

16 

17 2,121 

18 5,760 


3,726 25 

1,750 12 

980 8 

4,278 37 

3,780 42 

28 

56 


1.  Find  the  total  deposit  for  the  eight  days. 

2.  Find  the  total  number  of  depositors. 

3.  Find  the  average  daily  deposit. 

4.  Find  the  average  daily  number  of  depositors. 

5.  Find  the  average  deposit  for  all  the  depositors. 

6.  Tell  by  inspection  which  day  had   the  larger 
average  deposit  October  17  or  October  18. 

7.  Do  the  same  for  October  13  and  October  14, 


PROBLEMS  INVOLVING  DECIMAL  FRACTIONS     31 

VII 

A  man  receives  a  salary  of  $160  per  month. 

1.  VtTiat  is  his  annual  income? 

2.  How  much  rent  does  he  pay  annually  at  the  rate 
of  $22|  per  month? 

3.  Find  the  amount  of  his  fuel  bill  at  the  rate  of 
$7.75  per  month  for  eight  months. 

4.  What  is  his  annual  grocery  bill  at  the  rate  of 
$6.50  per  week? 

5.  Calculate  his  annual  gas  bill  and  light  bill,  the 
former  at  the  rate  of  $2.40  and  the  latter  at  the  rate 
of  $1.80  per  month. 

6.  Calculating  his  annual  expenditure  for  clothes 
$250,  and  his  incidental  expenses  $2.50  per  week,  how 
much  does  he  save  annually? 

7.  What  is  the  interest  on  his  annual  savings  for 
one  year,  if  it  is  .05  of  the  annual  savings? 

VIII 

John  P.  Walker  purchased  of  The  Model  Hardware 
Company,  Riverside,  Cal.,  Aug.  8,  1910,  the  following: 

6  dozen  bolts  at  50  cents  per  dozen ;  4  dozen  bolts  at 
2i  cents  each;  2  augers  at  $2.75;  3  gimlets  at  50  cents; 
60  pounds  of  nails  at  3|  cents;  2  garden  rakes  at  75 
cents;  2  hoes  at  35  cents;  2  hatchets  at  $1.25;  3  ham- 
mers at  75  cents;  2  saws  at  $2.50;  |  dozen  boxes  of 
tacks  at  5  cents;  1  hone  at  65  cents;  15  rods  of  wire  at 
12^  cents  per  yard;  2  express  wagons  at  $2.75  and 
$.90  respectively;  3  knives  at  40  cents;  1  lawn  mower, 
$6.25;    1  fishing  outfit,  $2.75;    and  2  razors  at  $2.40. 

Make  out  a  bill  and  receipt  it. 


32  ARITHMETIC  BY  PRACTICE 

IX 

William  Jones  purchased  the  following  articles  of 
Pettis  Dry  Goods  Company,  Indianapolis,  Ind.,  July 
10,  1911,  at  a  discount  of  .18  of  the  cost: 

3-piece  parlor  set  at  $55;  3  rockers  at  $9.50;  1  daven- 
port at  $40;  2  rockers  at  $5.50;  3  chairs  at  $8.50;  book 
case  at  $37.50;  1  dining  table  at  $25;  ^  dozen  chairs  at 
$3;  Ibufifet  at  $40.50;  1  kitchen  cabinet  at  $15;  1  break- 
fast table  at  $6.50;  3  chairs  at  $.75;  1  gas  range  at 
$26.75;  1  stand  at  $18.50;  2  bedsteads  at  $50  and  $35 
respectively;  1  dresser  at  $37.50;  1  chiffonier  at  $25.75; 
1  hall  tree  at  $14.50;  and  2  mirrors  at  $12.50.  Make 
out  a  bill  and  receipt  it. 

X 

Harry  Portsmouth  purchased  the  following  goods 
from  H.  A.  Mossman,  Newark,  New  Jersey,  June  22, 
1912,  at  a  discount  of  .10  of  the  cost  for  cash: 

3  dozen  handkerchiefs  at  25  cents  each;  2  umbrellas  at 
$3.50;  3  children's  hats  at  $1.50;  1  garment  at  $18.50; 
I  dozen  hose  at  37^  cents;  12  yards  lace  insertion  at 
15  cents;  15  yards  ribbon  at  12|  cents;  20  yards 
beading  at  8  cents;  3  spoons  at  $1.25;  2  pairs  side 
combs  at  90  cents;  2  pairs  silk  gloves  at  $2.75;  1  veil  at 
75  cents;  1  dozen  collars  at  12 J  cents;  6  spools  of 
thread  at  5  cents;  3  books  at  $1.20;  4  books  at  $.60; 
I  dozen  dolls  at  $.50;  8  toys  at  25  cents;  4  toys  at 
$1.25;  lady's  coat  at  $15;  2  rugs  at  $26.50;  15  yards  of 
carpet  at  75  cents;  18  yards  matting  at  35  cents; 
8  yards  linoleum  at  95  cents;  and  2  pairs  lace  curtains 
at  $8.50.     Make  out  a  bill  and  receipt  it. 


PROBLEMS  INVOLVING  DECIMAL  FRACTIONS  33 


This  drawing  represents  the  dial  of  an  electric  meter. 
The  contract  price  varies  from  7|  cents  to  10  cents 
per  kilowatt  hour. 

The  reading  as  indicated  above  is  1774  kilowatt 
hours. 

1.  What  is  the  reading  when  the  hand  on  No.  4  is 
between  2  and  3;  on  No.  3,  between  4  and  5;  on  No.  2, 
between  3  and  4;  and  on  No.  1,  at  5? 

2.  What  is  the  reading  when  the  hand  on  No.  4  is 
at  3;  on  No.  3,  at  0;  on  No.  2,  between  7  and  8;  and 
on  No.  1,  at  6? 

3.  Practice  reading  the  meter  with  the  hands  in 
different  positions. 

4.  The  reading  of  a  meter  at  successive  times  was 
476  and  512.  How  much  was  the  bill  for  the  month 
at  $.085  per  kilowatt  hour? 

5.  Read  your  electric  meter  for  two  successive 
months  and  calculate  the  bill  at  $.09  per  kilowatt  hour. 

6.  In  case  your  school  uses  electric  current,  read  the 
meter  at  intervals  of  a  week  and  determine  the  cost 
at  $.075  per  kilowatt  hour. 


34 


ARITHMETIC  BY  PRACTICE 


7.  Determine  the  position  of  the  hands  on  the  dials 
for  the  readings  in  problem  4. 

8.  Bring  an  electric  bill  from  home  and  determine 
the  position  of  the  hands  on  the  dials  for  the  given 
readings. 


100  THOUSAND 


XII 

10  THOUSAND 


I  THOUSAND 


This  drawing  represents  the  dials  of  a  gas  meter. 
The  rate  per  gas  is  from  $.60  to  $1.25  per  thousand 
cu.  ft. 

The  reading  as  indicated  above  is  68,200  cu.  ft. 

1.  Give  the  reading  when  the  hand  on  No.  3  is 
between  1  and  2;  on  No.  2,  between  3  and  4;  and  on 
No.  1,  at  7. 

2.  Give  the  reading  when  the  hand  on  No.  3  is  at 
0;  on  No.  2,  between  8  and  9;  and  on  No.  1,  at  5. 

3.  Practice  reading  the  meter  with  the  hands  in 
various  positions. 

4.  Give  two  readings  representing  successive  months 
and  calculate  the  gas  bill  for  the  month  at  $.90  per 
thousand  cu.  ft. 

5.  Read  your  gas  meter  for  two  successive  months 
and  calculate  the  bill. 


PROBLEMS  INVOLVING  DECIMAL  FRACTIONS     35 

6.  The  reading  of  a  meter  at  successive  times  was 
78,400  and  86,800.  How  much  was  the  bill  for  the 
month  at  $.85  per  thousand  cu.  ft.? 

7.  Determine  the  position  of  the  hands  on  the  dial 
for  the  readings  in  problem  6. 

^8.  Bring  a  receipted  gas  bill  and  determine  the 
position  of  the  hands  on  the  dial  for  the  given  readings. 

XIII 

A  certain  family  used  the  following  amount  of  gas 
and  electricity  during  the  year,  1912: 

Month  Gas  in  cu.  ft.  Electricity  in  k.w.  hours 

January 3,500 25 

February 3,300 24 

March 3,000 22 

April 3,200 18 

May 2,900 14 

June 2,800 8 

July 2,200 9 

August 2,100 9 

September 3,000 16 

October 3,100 20 

November 2,700 24 

December 2,500 28 

1.  What  was  the  gas  bill  for  the  year  at  $.90  per 
thousand  cu.  ft.? 

2.  Calculate  the  electric  bill  for  the  year  at  $.08  per 
kilowatt  hour. 

3.  Find  the  average  monthly  bill  for  gas. 

4.  Find  the  average  monthly  bill  for  electricity. 

5.  Find  the  bill  for  gas  for  January,  June,  and 
November,  respectively. 


36  ARITHMETIC  BY  PRACTICE 

6.  Find  the  bill  for  electricity  for  February,  July, 
and  December  respectively. 

7.  The  smallest  monthly  bill  for  electricity  is  how- 
many  hundredths  of  the  annual  bill  for  electricity? 

8.  Account  for  the  variations  in  the  monthly  bills 
for  electricity. 

XIV 

A  certain  family  used  the  following  amount  of  fuel 
during  the  year  1912: 

4  tons  of  Pocahontas  at  $4.75  per  ton,  bought  in  the 
summer. 

2  tons  of  anthracite  at  $7.75  per  ton,  bought  in  the 
summer. 

4  tons  of  coke  at  $5.50  per  ton,  bought  in  the  winter. 

2  tons  of  Pocahontas  at  $5.75  per  ton,  bought  in  the 
winter. 

1.  Find  the  total  cost  of  the  fuel  if  $.25  per  ton  is 
charged  for  carrying  in  the  coal  and  $.50  per  ton,  for 
carrying  in  the  coke. 

2.  The  cost  of  the  anthracite  is  how  many  hun- 
dredths of  the  cost  of  the  Pocahontas  bought  in  the 
summer? 

3.  The  cost  of  the  Pocahontas  bought  in  the  summer 
is  how  many  times  the  cost  of  the  Pocahontas  bought 
in  the  winter? 

4.  The  cost  of  the  anthracite  is  how  many  hun- 
dredths of  the  cost  of  all  the  Pocahontas? 

5.  The  cost  of  the  coke  is  how  many  hundredths  of 
the  cost  of  all  the  coal? 


PROBLEMS  INVOLVING  DECIMAL  FRACTIONS     37 

6.  The  cost  of  the  coke  is  how  many  hundredths  of 
the  cost  of  all  the  fuel? 

7.  Why  is  more  charged  for  carrying  a  ton  of  coke 
than  a  ton  of  coal? 

XV 

A  bought  an  automobile  for  $1500. 

1.  What  amount  of  tax  is  paid  for  the  automobile 
if  assessed  for  .55  of  the  cost,  at  $2.84  per  hundred? 

2.  If  the  machine  is  insured  for  three  years  for  .75  of 
the  cost,  at  $.80  per  hundred,  what  is  the  premium? 

3.  If  the  machine  depreciated  .35  of  its  value  the 
first  year,  how  much  was  it  then  worth? 

4.  If  the  machine  was  sold  for  $900,  the  selling  price 
is  how  many  hundredths  of  the  cost? 

5.  If  the  proceeds  were  invested  in  farm  land  at 
$75  per  acre,  how  many  acres  were  purchased? 

6.  For  how  much  per  acre  must  the  farm  be  rented 
to  yield  an  income  of  .07  of  the  investment? 

XVI 

Mr.  Black's  annual  net  income  from  his  farm  is  $600. 

1.  If  his  income  is  .08  of  his  investment,  what  is  his 
investment? 

2.  How  many  acres  in  the  farm  if  he  paid  $75  per 
acre? 

3.  How  much  tax  does  he  pay  if  he  is  assessed  .66f 
of  the  investment,  and  pays  at  the  rate  of  $2.15  per 
hundred? 


38  ARITHMETIC  BY  PRACTICE 

4.  He  raised  $712.50  worth  of  wheat,  at  the  rate  of 
$.95  per  bushel,  on  30  acres.  What  was  the  yield 
per  acre? 

5.  10  acres  of  oats  yielded  35  bushels  per  acre. 
The  oats  sold  for  $157.50.  What  was  the  selling  price 
per  bushel? 

6.  20  acres  of  corn  yielded  40  bushels  per  acre. 
How  much  was  it  worth  at  $.65  per  bushel? 

7.  The  value  of  the  corn  is  what  decimal  fraction  of 
the  value  of  the  wheat? 


XVII 

The  tax  rate  in  a  certain  city  is  $2.60  per  hundred 
dollars. 

1.  If  the  total  tax  from  assessable  property  is 
$200,000,  what  is  the  assessed  valuation  of  the  property? 

2.  What  is  the  real  value  of  the  property  if  the 
assessed  valuation  is  .625  of  the  real  value? 

3.  How  much  tax  does  Mr.  B.  pay  whose  property 
is  assessed  at  $12,500;  and  who  pays  for  one  poll  at 
the  rate  of  $3.25? 

4.  What  is  the  real  value  of  Mr.  B's  property? 

5.  If  the  above  City  had  been  required  to  raise 
$225,000  from  the  taxable  property,  what  would  have 
been  the  tax  rate? 

6.  Explain  just  what  determines  the  tax  rate? 

7.  Explain  the  manner  of  assessing  property? 

8.  What  is  meant  by  poll  tax? 


PROBLEMS  INVOLVING  DECIMAL  FRACTIONS     39 

XVIII 

A  horse  was  sold  for  $200. 

1.  The  seUing  price  is  1.25  of  the  cost  price.  What 
was  the  cost  of  the  horse? 

2.  If  the  horse  had  been  sold  for  $120,  the  selling 
price  would  have  been  how  many  hundredths  of  the 
cost? 

3.  The  horse  was  insured  against  fire  for  three  years, 
for  $150  at  the  rate  of  $.95  per  hundred.  What  was 
the  premium? 

4.  $200  is  how  many  hundredths  more  than  $120? 

5.  What  is  .0625  of  $150? 

6.  $250  is  how  many  hundredths  less  than  $300? 

7.  Find  .18  of  .45  of  $2500. 


XIX 

Mr.  Smith  bought  a  house  and  lot  for  $3900. 

1.  The  lot  cost  .625  as  much  as  the  house.  What 
was  the  cost  of  each? 

2.  The  value  of  the  lot  is  how  many  hundredths 
of  the  value  of  the  property? 

3.  The  value  of  the  property  is  how  many  hundredths 
of  the  value  of  the  house? 

4.  The  property  was  assessed  for  .68  of  the  value. 
Calculate  the  tax  at  the  rate  of  $2.42  per  hundred. 

5.  The  house  was  insured  for  three  years  for  .875  of 
its  value  at  the  rate  of  $.75  per  hundred.  What  was 
the  premium? 


40  ARITHMETIC  BY  PRACTICE 

6.  The  property  was  sold  at  a  gain  of  .22  of  the  cost. 
What  was  the  gain?     What  was  the  seUing  price? 

7.  If  it  had  been  sold  for  $3500,  the  loss  would  have 
been  how  many  hundredths  of  the  cost? 

XX 

I  purchased  a  lot  45  feet  wide  and  120  feet  deep  for 
$1200. 

1.  What  is  the  cost  per  front  foot? 

2.  What  is  the  cost  per  square  foot? 

3.  The  area  of  the  lot  is  what  decimal  fraction  of 
an  acre? 

4.  What  is  the  cost  per  square  rod? 

5.  For  how  much  must  I  sell  the  lot  to  gain  .24  of 
the  cost? 

6.  A  commission  agent  sold  it  for  $1450  and  charged 
.015  of  what  he  received  for  selling.  What  was  his 
commission? 

7.  I  invested  the  proceeds  in  R.R.  stock  at  $106  per 
share.  How  many  shares  did  I  buy  and  what  siun 
remained? 


CHAPTER  IV 
Problems  in  Applications  of  Percentage 

The  problems  in  this  chapter  involve  the  applica- 
tions of  percentage  as  well  as  a  review  of  common  and 
decimal  fractions.  Instructors  frequently  teach  the  ap- 
plications of  percentage  as  a  series  of  distinct  and  inde- 
pendent subjects.  As  a  result,  pupils  usually  solve  the 
problems  by  rule.  Definite  rules  are  learned  for  solv- 
ing problems  in  profit  and  loss;  definite  rules  for  com- 
mission; definite  rules  for  interest;  etc.  As  long  as 
the  pupil  remembers  the  rule,  he  gets  along  very  well, 
but  if  he  happens  to  forget  the  rule,  he  is  at  a  total 
loss  as  to  what  to  do. 

The  problems  in  this  chapter  serve  to  unify  the 
subject  of  percentage  in  all  of  its  applications.  The 
problems  in  the  different  applications  of  percentage 
are  not  solved  by  different  methods,  but  by  exactly 
the  same  method. 

When  a  certain  part  of  a  certain  number  of  dollars 
is  found,  it  is  called  gain  in  one  case;  loss  in  another 
case;  commission  in  another  case;  discount  in  another; 
interest  in  another;  tax  in  another;  etc.  The  method 
is  exactly  the  same,  but  the  name  for  the  result  is 
different.  Of  course  it  is  important  that  the  teacher 
explain  very  carefully  to  the  class  and  give  concrete 
illustrations  of  just  what  is  meant  by  the  terms,  com- 

41 


42  ARITHMETIC  BY  PRACTICE 

mission^  discount,  tax,  interest,  etc.  That  is  not  the 
purpose  of  this  text. 

The  problems  in  this  chapter  differ  in  nature  very- 
little  from  those  in  the  preceding  chapters.  The  new 
and  the  only  new  term  is  the  term  per  cent  (%).  But 
when  it  has  been  made  clear  that  whenever  the  sign 
''%''  is  written  with  a  number,  it  is  just  another  way 
of  expressing  the  same  number  written  as  a  decimal, 
or  as  a  conunon  fraction,  —  that,  for  example,  12%  of 
a  number  is  the  same  as  .12  of  the  number,  or  is  the 
same  as  yVV  of  the  niunber,  —  then  it  is  easy  to  see 
that  there  is  really  nothing  new  about  percentage. 
When  this  point  is  clearly  understood,  and  much  drill 
should  be  given  on  it,  then  the  problems  in  this  chapter 
may  be  solved  as  readily  and  in  the  same  manner  as 
those  in  Chapter  II  and  Chapter  III. 

In  solving  problems  in  percentage  the  pupil  should 
be  encouraged  to  use  that  form  (whether  per  cent, 
decimal  fraction,  or  common  fraction)  which  most 
appeals  to  him.  The  use  of  the  pernicious  100% 
method,  which  has  run  its  course,  should  be  discouraged. 

The  following  solutions,  which  are  the  solutions  to 
the  problems  in  set  I,  are  suggestive: 

1.  The  cost  X  1.20  =  $3600. 

.-.  The  cost  =  $3600  ^  1.20  =  $3000. 

Note.  —  Let  it  be  optional  with  the  pupil  to  divide 
by  1.20  or  by  f.  It  is  a  good  thing  to  do  both  at 
different  times. 

2.  The  cost  of  the  house  +  |  the  cost  of  the  house 
=  $3600. 


PROBLEMS  IN  APPLICATIONS  OF  PERCENTAGE    43 
/.  I  the  cost  of  the  house  =  $3600. 

900 

.-.  The  cost  of  the  house  =  $3600  -^  |  =  $360^- 
X  J  =  $2700. 

Note,  —  A  briefer  form  may  be  used  as  soon  as  the 
pupil  understands  the  work;   e.g., 

Let  C  =  cost. 
Then  C  +\C  =  $3600 
I C  =  $3600 
C  =  $3600  ^  I  =  $2700. 

30  0 

3.  The  insured  value  =  $2?ee-  X  i>  =  $2100. 
.-.  The  premium  =  $2100  X  .OOf  =  $15.75. 

Note.  —  Attention  should  be  called  to  the  fact  that 
this  is  not  a  practical  problem,  since  property  is  usually 
insured  for  a  period  of  three  or  five  years  at  a  certain 
rate  per  one  hundred  dollars. 

4.  The  assessed  valuation  =  $3600  X  |  =  $2880. 
.-.  The  amount  of  tax  =  $1.75  X  WV-  =  $50.40. 

5.  The  S.  P.  would  have  been  $3000  X  .90  =  $2700. 

6.  The  S.  P.  =  $3600  X  1.15  =  $4140. 

7.  Mr.  Brown's  loss  =  $3000  -  $2700  =  $300. 

Mr.  Smith's  gain  =-$4140  -  $3600  =  $540. 
$540  X  the  no.  of  per  cent  ^  ^^^ 

.:  Theno.of^percent  ^  ^3^^  _^  ^^^  ^  ^^^ 

:.  The  no.  of  per  cent  =  .55|  X  100  =  55f . 


44  ARITHMETIC  BY  PRACTICE 


Mr.  Brown  sold  his  house  and  lot  for  $3600  to  Mr. 
Smith. 

1.  If  Mr.  Brown  sold  his  property  at  a  gain  of  20%, 
how  much  did  he  pay  for  the  property? 

2.  If  the  lot  is  worth  ^  as  much  as  the  house,  how 
much  did  Mr.  Smith  pay  for  the  house? 

3.  Mr.  Smith  insured  the  house  for  I  of  what  he 
paid  for  it  at  f%.     How  much  premium  did  he  pay? 

4.  How  much  tax  did  Mr.  Smith  pay,  if  his  property 
was  assessed  for  f  of  its  value  at  the  rate  of  $1.75  per 
hundred? 

5.  If  Mr.  Brown  had  sold  his  property  at  a  loss  of 
10%,  how  much  would  he  have  received? 

6.  For  what  price  must  Mr.  Smith  sell  to  gain  15%? 

7.  Mr.  Brown's  loss  in  No.  5  is  what  %  of  Mr. 
Smith's  gain  in  No.  6? 

II 

John  and  Edwin  have  together  140  marbles. 

1.  If  John's  marbles  are  75%  of  Edwin's  marbles, 
how  many  marbles  has  each? 

2.  Edwin's  marbles  are  how  many  per  cent  of  John's 
marbles? 

3.  What  per  cent  of  his  marbles  must  Edwin  give 
John,  so  that  they  will  both  have  the  same  number? 

4.  Finly  and  Paul  wish  to  buy  enough  marbles  from 
John  and  Edwin  so  that  the  four  will  have  equal 
numbers.     How  many  should  each  sell? 

5.  If  they  increase  their  number  of  marbles  by 
120%,  how  many  marbles  will  they  then  have? 


PROBLEMS  IN  APPLICATIONS  OF  PERCENTAGE    45 

III 

Dan,  Leslie,  and  John  have  72  marbles. 

1.  Divide  the  above  marbles  in  the  ratio  of  3,  4, 
and  5. 

2.  What  %  of  all  the  marbles  has  each? 

3.  Dan's  marbles  are  how  many  %  of  John's? 

4.  Leslie's  are  how  many  %  of  Dan's? 

5.  John's  marbles  are  40%  of  how  many  marbles? 

6.  Dan's  marbles  plus  Leslie's  marbles  are  14%  of 
how  many  marbles? 

IV 

Mr.  Sankey  sold  his  house  and  lot  for  $4500. 

1.  If  Mr.  Sankey  gained  20%  in  the  above  trans- 
action, how  much  did  the  property  cost  him? 

2.  If  the  lot  cost  f  as  much  as  the  house,  what  was 
the  cost  of  each? 

3.  The  cost  of  the  lot  was  what  per  cent  of  the  cost 
of  the  house? 

4.  If  the  property  was  assessed  at  f  of  the  cost,  how 
much  tax  did  Mr.  Sankey  pay  at  $2.62  per  hundred? 

5.  The  house  was  insured  for  |  of  its  value.     How 
much  premium  was  paid  at  li%? 


A  man  sold  a  horse  for  $175. 

1.  If  he  gained  25%  of  the  cost,  what  was  the  cost 
of  the  horse? 

2.  How  much  did  he  gain?    Find  the  gain  in  two 
ways. 


46  ARITHMETIC  BY  PRACTICE 

3.  Had  he  sold  the  horse  for  $120,  what  per  cent 
would  he  have  lost? 

4.  What  would  have  been  the  sellmg  price,  had  he 
sold  it  at  a  gain  of  32%? 

5.  The  gain  in  the  second  problem  is  what  per  cent 
of  the  loss  in  the  third  problem? 

VI 

At  a  men's  furnishing  store,  the  selling  price  of  a 
suit  of  clothes  is  $25. 

1.  What  did  the  merchant  pay  for  the  suit  if  the 
selling  price  is  125%  of  the  cost? 

2.  If  the  suit  is  sold  for  $18,  what  per  cent  is  lost? 

3.  The  gain  in  the  first  problem  is  what  per  cent 
of  the  loss  in  the  second  problem? 

4.  Harry  earns  $80  per  month.  If  he  buys  the 
above  suit  for  10%  less  than  the  regular  selling  price, 
and  pays  $20  for  board;  what  per  cent  of  his  monthly 
earnings  has  he  left? 

5.  If  Harry  receives  an  increase  of  35%,  what  will 
be  his  increase  in  salary  for  one  year? 

VII 

A  commission  agent  sold  a  mill  for  $24,000. 

1.  The  agent  receives  $300  for  selling.  What  was 
his  rate  of  commission? 

2.  The  mill  was  owned  by  five  persons.  If  they 
held  equal  shares,  how  much  did  each  receive? 

3.  They  then  purchased  an  elevator  for  60%  of  the 
selling  price  of  the  mill.     What  did  the  elevator  cost? 


PROBLEMS  IN  APPLICATIONS  OF  PERCENTAGE    47 

4.  How  much  money  has  each  of  the  above  persons 
now? 

5.  How  many  acres  of  land  can  each  buy  at  $45 
per  acre? 

VIII 

In  a  certain  school  there  are  450  pupils. 

1.  There  are  f  as  many  boys  as  girls.  How  many 
are  boys  and  how  many  are  girls? 

2.  The  number  of  boys  is  what  per  cent  of  the  num- 
ber of  girls? 

3.  Had  the  number  of  boys  been  45  more,  it  would 
have  been  what  per  cent  of  the  number  of  girls? 

4.  f  of  f  of  I  of  the  number  of  boys  is  what  part  of 
I  of  f  of  If  of  the  number  of  girls? 

5.  If  10  boys  and  50  girls  withdraw,  the  number  of 
boys  is  what  per  cent  of  the  number  of  pupils? 

IX 

Mr.  A.  invested  $2500  in  a  mill. 

1.  A  dividend  of  25%  was  declared  but  12|%  were 
required  to  cover  expenses  and  2f  %  were  placed  in  the 
reserve  fund.     What  is  Mr.  A's  yearly  income? 

2.  If  he  was  assessed  j-  of  his  investment,  at  the 
rate  of  2f  %,  what  was  Mr.  A's  net  income? 

3.  Mr.  A  sold  his  interest  at  an  advance  of  20%,  and 
invested  in  a  farm  at  $50  per  acre.  How  much  was 
his  tax  reduced  if  his  farm  was  assessed  for  |  of  its 
value  at  the  same  rate? 

4.  If  he  rented  the  farm  for  $2.30  per  acre,  how  much 
was  his  net  income  increased  or  diminished? 


48  ARITHMETIC  BY  PRACTICE 

5.  He  sold  the  farm  at  an  advance  of  12|%  and 
invested  that  amount  in  a  house  for  which  he  paid 
10%  more  than  it  was  worth.  What  was  the  value  of 
the  house? 

X 

Mr.  C  owns  a  house  and  lot  for  which  he  paid  $3600. 

1.  A  commission  agent  sold  C's  property  for  $3000, 
and  charged  him  1|%  conamission.  What  was  the 
commission? 

2.  What  per  cent  did  C  lose? 

3.  If  the  conomission  agent  invested  the  proceeds 
in  sugar  at  5  cents  per  pound  after  deducting  his  com- 
mission of  2%,  how  many  pounds  did  he  buy?  (Is 
this  a  practical  problem?) 

4.  What  per  cent  would  C  have  gained  had  the 
property  been  sold  for  $4000? 

5.  How  much  would  the  agent  have  received  and 
how  much  would  he  have  invested  in  sugar? 

XI 

A  conmiission  agent  charged  $60  for  selling  a  house 
and  lot  at  the  rate  of  li%. 

1.  What  was  the  selling  price  of  the  property? 

2.  How  much  money  did  the  agent  turn  over  to  his 
Principal? 

3.  If  he  invested  the  net  proceeds  in  horses  at  $120 
apiece,  after  deducting  his  commission  of  1|%  for 
buying,  how  many  horses  did  he  buy? 

4.  How  many  pounds  of  sugar  can  he  buy  for  the 


PROBLEMS  IN  APPLICATIONS  OF  PERCENTAGE    49 

unexpended  sum  at  4J  cents  per  pound,  after  deducting 
his  commission  of  3%? 

5.  What  is  the  total  amount  of  the  agent's  com- 
mission in  the  above  transactions? 

XII 

A  man  purchased  a  house  for  $2800. 

1.  How  much  is  25%  of  75%  of  the  cost  of  the  house? 

2.  If  he  sells  the  house  for  $2500,  what  will  be  his 
loss  per  cent? 

3.  If  he  sells  it  for  $3000,  what  will  be  his  gain  per 
cent? 

4.  If  a  conmiission  agent  sells  the  house  for  $2900 
and  charges  1^%  for  selling,  how  much  money  will  he 
remit  to  the  owner? 

5.  If  the  owner  directs  the  commission  agent  to 
invest  the  net  proceeds  in  cows  at  $50  each  after 
deducting  his  commission  of  2%,  how  many  cows  can 
he  buy? 

6.  If  the  owner  of  the  above  house  was  assessed  f  of 
the  value  of  the  house,  what  amount  of  tax  did  he  pay 
at  $2.42  per  hundred? 

XIII 

Mr.  Smith  owns  a  house  and  lot  valued  at  $4800. 

1.  What  amount  of  tax  does  Mr.  Smith  pay  at  the 
rate  of  2.25  per  hundred,  if  he  is  assessed  |  of  the  value? 

2.  If  the  house  is  worth  f  of  the  property  and  is 
insured  for  full  value,  what  premium  does  Mr.  Smith 
pay  at  1|%? 


50  ARITHMETIC  BY  PRACTICE 

3.  If  a  commission  agent  sells  the  above  property 
at  a  gain  of  20%,  and  charges  a  commission  of  1|%, 
how  much  is  his  commission? 

4.  If  the  agent  invests  the  proceeds  in  horses  at 
$120  each  after  deducting  his  commission  of  2%,  how 
many  horses  can  he  buy? 

5.  What  is  20%  of  35%  of  $450? 

6.  160  is  what  per  cent  of  720? 

XIV 

I  bought  .375  of  a  section  of  land. 

1.  If  I  paid  $75  per  acre,  how  much  did  I  pay? 

2.  How  much  is  the  whole  section  worth  at  the 
same  rate? 

3.  What  is  the  value  of  the  south  §  of  the  S.  W. 
quarter? 

4.  What  is  the  perimeter  of  a  section  of  land  in  rods? 

5.  How  many  posts  if  placed  16  feet  apart  are 
required  for  a  fence  to  enclose  a  quarter  section? 

6.  If  I  sold  my  land  at  $15  per  acre  more  than  I  paid, 
what  per  cent  did  I  gain? 

7.  I  sold  the  land  May  13,  1908,  and  took  in  pay- 
ment a  note  due  Sept.  29,  1908.  How  much  did  I 
receive  when  the  note  was  due,  at  6%? 

XV 

Mr.  A  sold  a  horse  for  $150. 

1.  If  Mr.  A  gained  20%  of  what  he  paid  for  the 
horse,  what  was  his  gain? 


PROBLEMS  IN  APPLICATIONS  OF  PERCENTAGE     51 

2.  Had  he  received  $115,  what  would  have  been 
the  loss  %? 

3.  If  the  horse  is  assessed  at  $90,  how  much  tax  is 
paid  for  it  at  $2.60  per  hundred? 

4.  If  A  had  asked  $180  for  the  horse,  and  then  sold 
it  for  cash  at  a  discount  of  15  and  10%,  what  would 
have  been  his  gain  %? 

5.  If  A  had  taken  in  payment  a  note  for  $160,  due 
in  9  months,  16  days  at  6%,  what  would  he  have 
received  for  his  horse? 

XVI 

Mr.  Jackson  owns  a  section  of  land. 

1.  If  he  paid  $48,000  for  the  land,  what  was  the 
average  price  per  acre? 

2.  If  he  was  assessed  for  f  of  its  value,  what  amount 
of  tax  did  he  pay  at  $2.70  per  hundred? 

3.  Mr.  Jackson  sold  the  south  |  of  the  S.  W.  quarter 
at  $90  per  acre.  How  much  did  he  receive  and  what 
was  his  gain  per  cent? 

4.  If  he  had  taken  a  note  for  the  amount,  payable 
in  1  year  and  6  months,  with  interest  at  6%,  what 
amount  would  he  have  received? 

5.  If  he  had  had  the  note  discounted  at  a  bank, 
8  months  after  date,  at  8%,  what  amount  would  he 
have  received? 

6.  If  after  discounting  the  note,  a  commission  agent 
had  invested  the  proceeds  in  cattle  at  $40  apiece,  how 
many  could  he  have  purchased  after  deducting  his 
commission  of  2%? 


52  ARITHMETIC  BY  PRACTICE 

7.  If  he  invested  the  unexpended  sum  in  sugar  at 
5  cents  per  pound,  after  deducting  his  commission  of 
1|%,  how  many  pounds  could  he  buy? 

XVII 

Mr.  Clark  owns  a  house  and  lot  for  which  he  paid 
$3600. 

1.  The  lot  is  worth  |  as  much  as  the  house.  What 
is  the  value  of  each? 

2.  The  value  of  the  house  is  what  per  cent  of  the 
value  of  the  property? 

3.  The  value  of  the  lot  is  25%  of  what  sum? 

4.  What  amount  of  tax  does  Mr.  Clark  pay  at  $2.62 
per  hundred,  if  he  is  assessed  |  of  the  value? 

5.  He  has  his  house  insured  for  f  of  its  value.  How 
much  premium  does  he  pay  at  1|%? 

6.  If  Mr.  Clark  offers  the  property  for  sale  for 
$4500,  less  5  and  10%  for  cash,  how  much  would  he 
gain? 

7.  If  a  commission  agent  should  sell  the  property 
at  an  advance  of  15%,  what  would  be  Mr.  Clark's  net 
profit,  if  the  agent  charged  a  commission  of  1^%? 

8.  If  the  agent  be  instructed  to  invest  the  net 
proceeds  in  horses  at  $150  each,  after  deducting  his 
commission  of  2%  for  buying,  how  many  can  he  buy? 

XVIII 

Mr.  Jones  had  $2700. 

1.  He  invested  the  amount  in  a  house  and  lot, 
pa3dng  f  as  much  for  the  lot  as  for  the  house.  How 
much  did  he  pay  for  each? 


PROBLEMS  IN  APPLICATIONS  OF  PERCENTAGE    53 

2.  What  amount  of  tax  did  he  pay  at  $2.73  per 
hundred,  if  he  was  assessed  f  of  the  real  value? 

3.  How  much  was  his  premium  on  insuring  the 
house  at  11%,  if  he  had  it  insured  for  its  real  value? 

4.  Mr.  Jones  offers  the  property  for  sale  for  $3000, 
less  a  discount  of  10  and  5%.     How  much  will  he  lose? 

5.  A  conmiission  agent  sells  it  at  a  loss  of  5%,  charg- 
ing 1|%  commission.     What  is  the  agent's  commission? 

6.  The  agent  invested  the  proceeds  in  coffee  at 
30  cents  per  pound,  after  deducting  his  commission  of 
2%.     How  many  pounds  did  he  buy? 

XIX 

Mr.  Brown  sold  a  house  and  lot  for  $5600,  which 
was  at  a  loss  of  20%. 

1.  What  was  the  value  of  the  property? 

2.  The  lot  was  worth  f  as  much  as  the  house,  what 
was  the  value  of  each? 

3.  If  the  property  was  assessed  for  f  of  its  value, 
how  much  tax  did  Mr.  Brown  pay  at  $2.56  per  hundred? 

4.  If  he  had  taken  a  note  for  the  amount  received, 
due  in  8  months  with  interest  at  6%,  how  much  would 
he  have  received? 

5.  If  Mr.  Brown  had  had  the  note  discounted  at  a 
bank  3  months  after  date,  at  8%,  what  amount  would 
he  have  received? 

XX 

Mr.  Smith  purchased  a  lot  for  $3000. 
1.   If  Mr.  Smith  paid  80%  of  the  value  of  the  lot, 
what  was  the  value? 


54  ARITHMETIC  BY  PRACTICE 

2.  ^  of  f  of  f  of  what  Mr.  Smith  paid  is  -^^  of  what 
Mr.  Brown  paid  for  his  lot.  How  much  did  Mr. 
Brown  pay? 

3.  Mr.  Smith's  lot  cost  what  per  cent  of  Mr.  Brown's 
lot? 

4.  What  is  the  tax  on  both  lots  if  they  were  assessed 
at  I  of  their  value,  at  the  rate  of  $2.30  per  hundred? 

5.  If  Mr.  Smith  asks  $4500,  but  sells  his  lot  at  a 
discount  of  15  and  5%,  how  much  does  he  receive? 

A      3.1   V  -^  —  ? 
t>.     2Z  X  ^^  -    ( 

XXI 

A  man  bought  a  house  and  lot  for  $6000. 

1.  If  the  house  is  worth  f  as  much  as  the  lot,  what 
is  each  worth? 

2.  If  the  house  and  lot  were  sold  for  20%  less  than 
the  asking  price,  what  was  the  asking  price? 

3.  If  the  man  who  sold  the  house  paid  $4500  for  the 
property,  what  was  his  gain  %? 

4.  If  the  agent  who  sold  the  house  for  $6000  received 
$75  commission,  what  was  his  rate  of  commission? 

5.  How  much  premium  does  the  man  pay,  if  he  has 
his  house  insured  for  $3000  at  f%? 

6.  His  property  is  assessed  at  f  the  value.  What  is 
the  amount  of  his  tax  at  $2.25  per  hundred  dollars? 

XXII 

A  man  bought  a  house  and  lot  for  $4500. 
1.   If  the  lot  is  worth  ^  as  much  as  the  house,  what 
is  the  value  of  each? 


PROBLEMS  IN  APPLICATIONS  OF  PERCENTAGE    55 

2.  What  insurance  does  the  owner  pay  at  1|%  if 
the  house  is  insured  for  f  of  its  value? 

3.  If  the  property  is  assessed  at  |  of  its  value,  at 
$2.43  per  hundred,  what  is  the  amount  of  the  tax? 

4.  If  the  property  sold  for  $4200,  what  was  the 
loss  %? 

5.  Had  the  owner  of  the  property  asked  $6000  and 
then  sold  it  at  a  discount  of  5  and  10%,  what  would 
have  been  the  gain  %? 

XXIII 

A  man  bought  a  house  and  lot. 

1.  If  the  house  cost  $2400  and  the  lot  f  as  much, 
what  was  the  cost  of  both? 

2.  He  sold  the  house  and  lot  for  $3900.  What  was 
the  gain  %? 

3.  f  of  3^  of  the  cost  of  the  property  is  what  %  of 
1^  of  the  selling  price? 

4.  If  the  man  had  taken  a  note  for  the  property 
for  $3400  for  2  years,  7  months,  18  days  at  6%  interest, 
what  amount  would  he  have  received? 

5.  What  was  the  amount  of  the  tax  on  the  property 
at  $2.70  per  hundred,  if  it  was  assessed  at  f  of  the  cost? 

XXIV 

A  man  owns  a  house  and  lot. 

1.  If  the  house  cost  him  $2700  and  the  lot  cost  f 
as  much  as  the  house,  what  is  their  total  cost? 

2.  If  they  advance  in  price  and  he  sells  them  at 
33|%  profit,  what  does  he  receive  for  them? 


56  ARITHMETIC  BY  PRACTICE 

3.  If  he  takes  a  man^s  note  for  them,  what  will  be 
its  amount  in  8  months  at  6%? 

4.  If  he  should  invest  the  amount  of  the  note  when 
it  is  due  in  a  farm  and  sell  the  farm  for  $3600,  what 
would  be  his  per  cent  of  loss  on  the  farm? 

5.  The  selling  price  of  the  farm  is  how  many  per  cent 
of  the  original  cost  of  the  house  and  lot? 

XXV 

A  man  sold  120  bushels  of  wheat  at  95  cents  per 
bushel  and  600  bushels  of  corn  at  62  cents  per  bushel. 

1.  How  much  did  he  receive? 

2.  He  invested  the  money  in  horses  at  $115  each. 
How  many  horses  did  he  buy? 

3.  He  sold  the  horses  at  a  gain  of  20%.  How  much 
did  he  receive? 

4.  If  he  had  taken  a  note  for  the  amount  for  8 
months  at  6%,  how  much  would  he  have  received? 

5.  How  much  would  he  have  received,  had  he  dis- 
counted the  note  at  a  bank  at  8%,  3  months  after  date? 

6.  State  two  principles  of  division. 

XXVI 

A  has  $150  and  B  has  $240. 

1.  A^s  money  is  how  many  %  of  B's? 

2.  B's  money  is  what  %  of  A's? 

3.  A's  money  is  what  %  of  A's  plus  B's? 

4.  I  of  A's  money  is  what  part  of  f  of  B^s? 

5.  B  must  give  what  part  of  his  money  to  A  so  that 
both  will  have  equal  sums? 


PROBLEMS  IN  APPLICATIONS  OF  PERCENTAGE    57 

6.  If  B  loses  $20,  how  much  must  A  earn  to  have 
as  much  as  B? 

7.  If  A  and  B  take  then*  money,  and  divide  it  in  the 
ratio  of  6  to  7,  how  much  will  each  receive? 

XXVII 

Mr.  Siebe  invested  $5000  in  a  mill. 

1.  If  his  annual  income  was  $450,  what  rate  per  cent 
did  he  receive  on  his  investment? 

2.  What  amount  of  tax  did  he  pay  at  the  rate  of 
$.027  on  the  dollar? 

3.  He  sold  his  stock  at  an  advance  of  12§%,  how 
much  did  he  receive? 

4.  He  invested  this  amount  in  mining  stock,  which 
paid  a  semi-annual  income  of  4|%.  How  much  did 
he  increase  his  annual  income? 

5.  He  then  sold  his  stock  at  a  discount  of  8%,  how 
much  did  he  receive? 

6.  He  employed  an  agent  to  invest  this  amount  in 
land  at  $70  per  acre,  after  deducting  his  commission 
of  1^%.     How  many  acres  did  he  buy? 

XXVIII 

Mr.  M.  had  property  valued  at  $3200. 

1.  A  commission  agent  sold  the  property  at  an 
advance  of  25%.     What  was  his  commission  at  li%? 

2.  The  agent  invested  the  proceeds  in  horses  at 
$115  each,  after  deducting  his  commission  of  2%. 
How  many  horses  did  he  buy? 


58  ARITHMETIC  BY  PRACTICE 

3.  He  purchased  sheep  with  the  balance  after  de- 
ducting his  commission  of  2%.  How  many  sheep  did 
he  buy  at  $4  apiece? 

4.  He  invested  the  balance  in  sugar  at  5  cents  per 
pound,  after  deducting  his  commission  of  2%.  How 
many  pounds  of  sugar  did  he  buy? 

5.  What  is  8%  of  40%  of  85%  of  $1600. 

XXIX 

Mr.  C,  who  owns  a  house  and  lot,  pays  $71.43  tax. 

1.  If  he  pays  a  poll  tax  of  $2.43,  what  is  the  assessed 
valuation  of  his  property  at  $2.30  per  hundred? 

2.  If  the  property  is  assessed  at  |  of  the  real  value, 
what  is  the  value? 

3.  The  house  is  worth  f  as  much  as  the  lot.  What 
is  the  value  of  each? 

4.  What  premium  does  Mr.  C  pay  if  his  house  is 
insured  for  f  of  its  value  at  li%? 

5.  If  a  commission  agent  sells  the  property  for 
$4100,  charging  1^%,  what  is  Mr.  C's  net  gain  %? 

6.  If  Mr.  C  had  sold  the  property  for  $4200  by 
taking  in  payment  a  60-day  note,  which  he  might  have 
discounted  at  a  bank  at  6%,  would  it  have  been  better 
than  the  commission  agent's  offer  and  how  much? 

XXX 

Mr.  Williams  has  $4500. 

1.  Divide  the  above  sum  in  the  ratio  of  3,  4,  and  5. 

2.  He  invested  the  amount  in  a  plot  of  ground  con- 
taining 12  acres,  with  a  house  on  it.     Find  the  value 


PROBLEMS  IN  APPLICATIONS  OF  PERCENTAGE    59 

of  the  house,  and  the  land  per  acre,  if  the  house  was 
worth  f  as  much  as  the  land. 

3.  He  was  assessed  ^  of  the  real  value.  How  much 
tax  did  he  pay  at  $2.73  per  hundred? 

4.  He  offered  to  sell  the  property  for  $5400,  less  a 
discount  of  2 J  and  5%.  How  much  would  he  have 
gained  or  lost? 

5.  If  he  had  sold  the  property  for  $4800  by  taking 
in  payment  a  note  payable  in  one  year  and  four  months, 
with  interest  at  6%,  how  much  would  he  have  received? 

6.  If  he  had  had  the  note  discounted  at  a  bank  at 
8%,  10  months  after  date,  how  much  would  he  have 
received? 

XXXI 

Mr.  Fox  sold  his  house  and  lot  for  $4500. 

1.  If  Mr.  Fox  made  25%  by  the  transaction,  how 
much  did  he  pay  for  the  property? 

2.  If  he  paid  f  as  much  for  the  lot  as  for  the  house, 
what  was  the  cost  of  each? 

3.  The  cost  of  the  lot  is  what  %  of  the  selling  price 
of  the  property? 

4.  If  Mr.  Fox  paid  tax  on  an  amount  equivalent  to 
-|  of  what  he  received  for  the  property,  how  much  did 
he  pay  at  $2.40  per  hundred? 

5.  Had  Mr.  Fox  taken  an  interest-bearing  note  for 
the  amount  he  received,  for  1  year,  10  months,  12  days 
at  6%,  what  sum  would  'he  have  received? 

6.  If  he  had  had  the  note  discounted  one  year  after 
date  at  8%,  what  amoimt  would  he  have  received? 


60  ARITHMETIC  BY  PRACTICE 

XXXII 

A  man  bought  a  house  and  lot,  and  paid  $1400  for 
the  lot. 

1.  If  the  house  is  worth  If  times  as  much  as  the 
lot,  what  is  their  total  value? 

2.  The  cost  of  the  lot  is  what  %  of  the  cost  of  the 
property? 

3.  The  property  was  assessed  at  H  of  the  value. 
How  much  tax  did  he  pay  at  $2.25  per  hundred? 

4.  If  he  had  the  house  insured  for  f  of  its  value, 
how  much  premium  did  he  pay  at  1^%? 

5.  If  he  sold  the  property  for  $4000,  taking  in 
payment  an  8  months'  interest-bearing  note,  with 
interest  at  6%,  how  much  did  he  receive? 

6.  If  he  had  had  the  note  discounted  at  a  bank 
2  months  after  date  at  8%,  how  much  would  he  have 
received? 

XXXIII 

Mr.  A  sold  a  house  for  $5000  through  a  commission 
agent.  The  agent  received  $87.50.  Mr.  A  had  paid 
$4500  for  the  house. 

1.  What  was  A's  net  gain  per  cent? 

2.  What  was  the  agent's  rate  %  of  commission? 

3.  The  selUng  price  is  what  per  cent  of  the  cost? 

4.  Had  the  selling  price  been  2%  more  what  would 
it  have  been? 

5.  If  the  agent  had  asked  $6000,  but  had  sold  it 
for  15  and  10%  off,  what  would  have  been  the  selling 
price? 


PROBLEMS  IN  APPLICATIONS  OF  PERCENTAGE    61 

XXXIV 

The  assessed  valuation  of  a  town  is  $2,450,000.  A 
tax  of  $41,800  is  necessary  to  defray  expenses.  There 
are  5000  polls  at  $1.50  each. 

1.  What  is  the  rate  of  taxation  ? 

2.  What  is  Mr.  C's  tax  who  owns  a  farm  assessed 
at  $3500,  and  pays  for  one  poll? 

3.  Mr.  D's  tax  is  $57.60.  He  pays  for  one  polL 
What  is  the  assessed  valuation  of  his  property? 

XXXV 

Mr.  A  had  an  interest  of  $3000  in  a  corporation. 

1.  If  at  the  end  of  the  year,  the  corporation  made 
a  gross  gain  of  18%  but  required  7%  to  cover  expenses 
and  placed  2%  in  the  reserve  fund,  what  income  did 
Mr.  A  receive? 

2.  If  Mr.  A  paid  f %  insurance  and  taxes  at  the 
rate  of  $2.25  per  hundred,  how  much  is  his  net  income? 

3.  Mr.  A  invested  the  $3000  in  a  farm  at  $40  per 
acre.  He  pays  a  tax  of  $1.75  per  hundred  for  f  of  its 
value.  He  receives  an  income  of  $2.50  per  acre.  Has 
he  increased  or  diminished  his  net  income  and  how 
much? 

4.  Mr.  A  sold  the  farm  at  a  loss  of  12|%.  How 
much  did  he  receive? 

5.  Had  he  taken  a  note  for  that  amount  for  8  months 
and  15  days  with  interest  at  6%,  what  amount  would 
he  have  received? 

6.  State  two  principles  of  multiplication. 


62  ARITHMETIC  BY  PRACTICE 

XXXVI 

Mr.  Adams  bought  a  lot  for  $1200. 

1.  He  built  a  house  on  this  lot  which  cost  187^% 
as  much  as  the  lot.  What  was  the  cost  of  the  lot  and 
house? 

2.  If  the  property  was  assessed  at  f  of  the  value, 
what  amount  of  tax  did  Mr.  Adams  pay  at  the  rate 
of  $2.24  per  hundred? 

3.  How  much  premium  did  he  pay  for  insuring  his 
house  for  |  of  its  value  at  the  rate  of  80  cents  per 
hundred  for  three  years? 

4.  He  sold  his  property  for  $4140.  What  %  did  he 
gain? 

5.  If  he  had  taken  a  note  for  this  amount  due  in 
8  months  with  interest  at  6%,  what  amount  would 
he  have  received? 

XXXVII 

Mr.  Davis  bought  a  horse  and  a  carriage  for  $264. 

1.  The  horse  cost  |  as  much  as  the  carriage.  What 
was  the  cost  of  each? 

2.  The  cost  of  the  carriage  is  what  %  of  the  cost 
of  the  horse? 

3.  Mr.  Davis  sold  the  horse  and  the  carriage  at  a  loss 
of  12J%.     How  much  did  he  receive? 

4.  If  he  took  a  60-day  note  with  interest  at  6%, 
what  amount  did  he  receive? 

5.  If  he  had  had  the  note  discounted  at  8%  20  days 
after  date,  what  amount  would  he  have  received? 


PROBLEMS  IN  APPLICATIONS  OF  PERCENTAGE    63 

XXXVIII 

Mr.  James  has  $3900. 

1.  Divide  this  sum  in  the  ratio  of  J,  |,  and  i. 

2.  He  invested  the  amount  in  a  house  and  lot  paying 
if  as  much  for  the  house  as  for  the  lot,  how  much  did 
he  pay  for  each? 

3.  What  amount  of  tax  did  he  pay  if  he  was  assessed 
f  of  the  real  value,  the  rate  of  taxation  being  $2.74  per 
hundred? 

4.  A  commission  agent  sold  the  property  at  a  gain 
of  15%,  charging  1|%  coromission.  What  was  his 
commission? 

5.  He  invested  the  net  proceeds  in  horses  at  $150 
each  after  deducting  his  commission  of  2%.  How 
many  horses  did  he  purchase? 

6.  The  commission  agent  invested  the  unexpended 
sum  in  coffee  at  20  cents  per  pound  after  deducting  his 
conamission  of  2%.     How  many  pounds  did  he  buy? 

XXXIX 

Twenty  boys  organize  an  athletic  club  with  a  capital 
of  $160. 

1.  How  much  does  each  boy  contribute  if  they  share 
equally? 

2.  If  the  above  capital  is  divided  into  50  cent  shares, 
how  many  shares  will  there  be? 

3.  Frank  Thomas,  the  president,  takes  30  shares  at 
par.     What  is  the  value  of  his  stock? 

4.  After  the  members  have  subscribed  for  all  the 


64  ARITHMETIC  BY  PRACTICE 

stock  they  care  for,  12  shares  remain.  They  are  bought 
by  a  non-member  at  15%  above  par.  How  much 
does  he  pay  for  them? 

5.  One  of  the  original  stockholders  retires  from  the 
club,  and  sells  his  stock  to  the  captain  at  a  discount 
of  20%.  If  he  had  6  shares,  how  much  did  he  lose  by 
his  investment? 

6.  How  many  shares  can  be  bought  for  $4.05  if  they 
are  bought  at  10%  below  par? 

7.  At  the  end  of  the  season,  the  members  of  the 
club  found  that  they  had  $16  in  the  treasury,  over  and 
above  expenses.  If  this  was  divided  among  the  stock- 
holders in  proportion  to  the  number  of  shares  they 
held,  how  much  of  the  dividend  would  John  Mason 
receive,  who  had  10  shares? 

8.  At  the  beginning  of  the  next  season,  the  club 
levied  an  assessment  of  12|%  to  cover  initial  expenses. 
How  much  was  paid  on  each  share? 

9.  One  of  the  original  members  at  once  sold  his  stock 
at  60  cents  per  share.  What  was  the  gain  %  on  the 
par  value  of  the  stock? 

10.  What  was  the  gain  %  on  the  total  investment 
of  the  stock? 

XL 

Mr.  D  has  $6000.  Which  of  the  following  invest- 
ments will  bring  the  largest  income? 

1.  In  8%  stock  at  150. 

2.  In  7%  stock  at  125. 

3.  In  5|%  stock  at  par. 

4.  In  4^%  stock  at  20%  discount. 


PROBLEMS  IN  APPLICATIONS  OF  PERCENTAGE    65 

6.   In  3%  stock  at  40%  discount. 

6.  In  general  merchandise  with  a  guaranteed  income 
of  5f  %. 

7.  In  bonds  bought  at  a  premium  of  20%,  bringing 
an  income  of  6|%. 

8.  In  a  farm  at  $75  per  acre  with  a  net  income  of 
$4.25  per  acre. 


CHAPTER  V 

Problems  in  Measurement  and  Mensuration 

The  following  problems  are  those  which  are  usually 
given  under  the  subject  of  mensuration,  which  includes 
problems  of  carpeting,  of  papering  rooms,  etc.  The 
following  solutions,  which  are  solutions  to  the  problems 
in  set  V  are  suggestive: 

1.  The  no.  of  posts  =  ^  +  Y  +  ^F-  +  ^|^  = 

5+5+23+23     =56. 

Note.  —  The  above  solution  may  require  some  ex- 
planation by  the  teacher.  Common  sense  must  always 
take  precedence  in  the  solution  of  problems. 

2.  The  cost  of  the  posts  = 

i-X>X^X56  X^  X  $2^=  $16.13. 

-S-6r 

Note.  —  The  answer  should  be  given  to  the  nearest 
cent. 

3.  The  perimeter  =  2  (180  +  40)  =  440  ft. 

.-.  The  cost  of  the  lumber  = 
11 

^  X>  X^  X  xi^  X  $1.95  =  $21.45. 

20 

4.  The  no.  of  sq.  yds.  =  ^^ ^  ^^  =  800. 

:.  The  cost  of  sodding  =  $.15  X  800  =  $120. 

66 


PROBLEMS  IN  MEASUREMENT  AND  MENSURATION  67 

5.   The    length    of    the    longest    string    in    feet  = 
VI8O2  +  402  =  V44,000  =  209.76. 

Note.  —  This  should  be  accompanied  by  a  drawing. 


6.   The    distance    in    feet  =  VlSO^  +  40^  +42  = 
V44,016  =  209.799. 


Mr.  D  purchased  a  lot  60  feet  wide  and  100  feet  deep. 

1.  How  many  posts  are  required  to  enclose  the  lot 
with  a  fence,  if  the  posts  are  placed  8  feet  apart? 

2.  What  will  they  cost  at  $1.50  per  hundred  board 
feet,  if  they  are  8  feet  by  4  inches  by  3  inches? 

3.  If  the  fence  is  5  boards  high,  what  will  the  boards 
cost  at  $1.75  per  hundred? 

4.  What  will  it  cost  to  sod  the  lot  at  15  cents  per 
square  yard? 

5.  The  cost  of  the  posts  is  what  %  of  the  cost  of 
the  boards? 

6.  The  cost  of  the  lawn  is  what  %  of  the  whole  cost 
of  improvements? 

II 

Mr.  A  purchased  a  plot  of  ground  250  feet  north  and 
south  and  240  feet  east  and  west. 

1.  How  much  did  it  cost  at  $90  per  acre? 

2.  Mr.  A  planned  an  alley  10  feet  wide  through  the 
middle  of  the  lot  east  and  west.  How  many  square 
yards  in  the  alley? 


68  ARITHMETIC  BY  PRACTICE 

3.  He  then  laid  out  lots  on  each  side  30  feet  wide. 
If  he  sold  i  of  them  at  $50  apiece  an4  the  other  half 
at  $60  apiece  how  much  did  he  receive? 

4.  What  was  his  gain  per  cent? 

5.  If  the  posts  for  fences  to  enclose  all  the  lots  are 
placed  6  feet  apart,  how  many  will  be  required? 

6.  How  many  rods  of  fence  will  be  required  to 
enclose  all  the  lots? 


Ill 

A  certain  field  contains  40  acres. 

1.  If  the  field  is  rectangular,  and  120  rods  long;  how 
wide  is  it? 

2.  If  it  is  a  square,  what  is  the  length  of  one  side? 

3.  If  it  is  a  general  parallelogram,  160  rods  long, 
how  wide  is  it? 

4.  If  it  is  a  trapezoid,  and  the  simi  of  the  parallel 
sides  is  200  rods,  what  is  the  altitude? 

5.  What  is  the  perimeter  of  each  of  the  fields? 


IV 

I  purchased  a  plot  of  ground  45  rods  by  40  rods  for 
$900. 

1.  How  much  did  I  pay  per  acre? 

2.  Beginning  at  one  corner,  I  sold  10  contiguous 
lots  each  40  feet  wide  by  120  feet  deep,  for  $50  each. 
How  many  acres  did  I  sell? 

3.  What  was  my  gain  %? 


PROBLEMS  IN  MEASUREMENT  AND  MENSURATION  69 

4.  The  perimeter  of  the  10  lots  is  what  %  of  the 
perimeter  of  the  remaining  plot  of  ground? 

5.  If  an  alley  twelve  feet  wide  be  built  around  the 
two  sides  of  the  sold  piece  of  land,  how  many  square 
yards  would  it  contain? 


The  dimensions  of  a  lot  are  40  feet  by  180  feet. 

1.  How  many  posts  are  required  for  a  fence  to  sur- 
round the  lot,  if  they  are  placed  8  feet  apart? 

2.  If  the  posts  measure  4  inches  by  6  inches  by 
6  feet,  what  will  they  cost  at  $2.40  per  hundred  board 
feet? 

3.  A  six  board  fence  is  put  around  the  lot.  What  is 
the  cost  of  the  lumber  at  $1.95  per  hundred? 

4.  What  is  the  cost  of  sodding  the  lot,  at  15  cents 
per  square  yard? 

5.  What  is  the  length  of  the  longest  string  that  may 
be  stretched  across  the  lot? 

6.  If  the  posts  are  two  feet  in  the  ground,  what  is 
the  distance  from  the  top  of  a  corner  post  to  the  opposite 
corner  of  the  lot? 

VI 

A  certain  field  contains  30  acres. 

1.  If  the  field  is  rectangular,  and  80  rods  long,  how 
wide  is  it? 

2.  What  is  the  perimeter?    What  is  the  diagonal? 

3.  If  the  field  is  in  the  shape  of  an  isosceles  triangle, 
with  base  100  rods,  what  is  the  altitude? 


70  ARITHMETIC  BY  PRACTICE 

4.  What  is  the  perimeter? 

5.  If  the  field  is  circular  in  shape,  what  is  the  diam- 
eter? 

6.  Which  of  the  fields  will  require  the  least  fencing, 
and  by  how  many  rods? 

VII 

Mr.  Brown  purchased  a  lot  40  feet  wide  by  120  feet 
deep,  for  $1500.  He  built  a  house  on  this  lot,  which 
cost  him  $3500. 

1.  If  the  house  covered  a  space  of  1500  square  feet, 
what  will  it  cost  to  sod  the  yard  at  15  cents  per  square 
yard? 

2.  The  parlor  is  16  feet  by  14  feet  by  12  feet.  What 
will  it  cost  to  paper  the  walls  and  ceiling  at  75  cents 
per  roll  put  on,  and  the  border  costing  30  cents  per 
yard?    A  roll  is  24  feet  long  and  18  inches  wide. 

3.  How  much  will  a  carpet  cost  for  the  floor  at  $2.25 
per  yard,  laying  it  the  more  economical  way,  if  it  is 
f  yard  wide? 

4.  The  sitting  room  is  15  feet  by  12  feet  by  12  feet. 
What  will  it  cost  to  paper  the  walls  and  ceiling  at 
60  cents  per  roll  put  on,  and  the  border  costing  25  cents 
per  yard? 

5.  What  will  the  carpet  cost  for  this  floor  at  $2.00 
per  yard,  if  it  is  f  yard  wide? 

6.  Each  of  the  two  bedrooms  is  14  feet  by  12  feet 
by  12  feet.  What  will  it  cost  to  paper  the  walls  and 
ceihngs  of  the  same  at  40  cents  per  roll  put  on,  with  a 
border  at  15  cents  per  yard? 


PROBLEMS  IN  MEASUREMENT  AND  MENSURATION  71 

7.  What  will  be  the  cost  of  the  matting  for  the  two 
rooms  at  40  cents  per  yard,  the  matting  being  1  yard 
wide? 

8.  The  dining  room  is  16  feet  by  15  feet  by  12  feet. 
Find  the  cost  of  papering  the  walls  and  ceiling  at 
70  cents  per  roll  put  on,  with  a  border  at  35  cents  per 
yard. 

9.  What  will  the  carpet  cost  to  cover  the  floor  at 
$2.15  per  yard,  if  it  is  f  yard  wide? 

10.  The  kitchen  is  12  feet  by  12  feet  by  12  feet. 
What  will  it  cost  to  paint  the  walls  and  ceiling  at 
20  cents  per  square  yard? 

11.  What  will  the  linoleum  cost  at  75  cents  per  yard 
for  every  yard  in  width? 

12.  If  Mr.  Brown  furnished  the  house  with  $800 
and  if  $150  be  allowed  for  incidental  expenditures, 
what  are  his  total  expenses? 

13.  If  his  property  is  assessed  at  60%  of  what  he 
paid,  how  much  tax  does  he  pay  at  $2.37  per  hundred? 

14.  If  he  has  the  house  and  personal  property  in- 
sured for  I  of  its  value  at  1|%,  how  much  premium 
does  he  pay? 

15.  If  the  lot  is  a  corner  lot,  how  much  will  the  walks 
cost  if  they  are  4  feet  wide,  at  10  cents  per  square  foot? 

VIII 

A  school  room  is  35  feet  long,  28  feet  wide,  and  14 
feet  high. 

1.  How  many  square  feet  in  the  ceiling? 

2.  How  many  feet  in  the  perimeter? 


72  ARITHMETIC  BY  PRACTICE 

3.  How  many  square  yards  in  the  walls? 

4.  The  width  is  how  many  %  of  the  length? 

5.  The  perimeter  is  how  many  %  of  the  height? 

6.  The  area  of  the  ceiling  is  125%  of  how  many 
square  feet? 


IX 

I  built  a  barn  60  feet  long,  40  feet  wide  and  20  feet 
high  to  the  top  of  the  siding.  It  is  covered  with  a 
comb-shaped  roof  which  rises  to  a  point  15  feet  above 
the  siding. 

1.  What  is  the  cost  of  the  lumber  for  the  siding  and 
gables  at  $1.50  per  hundred? 

2.  What  is  the  length  of  the  rafters  if  they  are  made 
to  project  one  foot  from  the  edge  of  the  barn? 

3.  How  many  rafters  are  required  if  they  are  placed 
two  feet  apart  and  the  roof  is  made  to  project  two  feet 
at  each  gable? 

4.  If  the  shingles  are  5  inches  wide  and  are  laid 
4  inches  to  the  weather,  what  do  they  cost  at  $4.50 
per  thousand?     (A  double  row  to  start  with.) 

5.  The  floor  of  the  loft  is  6  feet  below  the  top  of  the 
siding.     How  many  cubic  feet  in  the  loft? 

6.  How  many  bushels  of  wheat  can  be  placed  in  the 
loft,  if  the  wheat  is  placed  5  feet  deep? 

7.  What  is  the  diagonal  of  the  barn? 

8.  If  I  wish  to  make  a  bin  in  the  barn  to  hold  500 
bushels  of  corn,  how  long  must  it  be,  if  it  is  10  feet 
wide  and  8  feet  deep? 


PROBLEMS  IN  MEASUREMENT  AND  MENSURATION  73 

X 

A  plot  of  ground  30  rods  long  and  20  rods  wide  is 
surrounded  by  a  wire  fence.  The  posts  are  placed 
15  feet  apart,  and  the  fence  consists  of  6  wires.  A 
barn  50  feet  long  and  30  feet  wide  stands  lengthwise 
of  the  plot  in  the  center. 

Its  roof  is  comb-shaped  and  rises  20  feet  at  the 
ridge.  This  roof  projects  1  foot  at  the  eaves  and 
gables.     The  side  walls  of  the  barn  are  16  feet  high. 

1    How  many  posts  are  required  to  build  the  fence? 

2.  The  posts  are  8  feet  long  and  4  inches  square. 
How  many  board  feet  do  they  contain? 

3.  What  is  the  cost  of  the  wire  at  one  cent  per  yard? 

4.  What  portion  of  the  lot  is  covered  by  the  barn? 

5.  How  much  siding  will  the  barn  require  including 
the  gables? 

6.  How  long  are  the  rafters? 

7.  What  will  the  shingles  cost  at  $3  per  thousand,  if 
they  are  4  inches  wide  and  are  placed  4|  inches  to 
the  weather?     (A  double  row  to  start  with.) 

8.  How  much  space  is  there  in  the  loft  if  its  floor  is 
3  feet  below  the  top  of  the  side  walls? 

XI 

I  purchased  a  lot  60  feet  wide  and  100  feet  deep, 
east  and  west.  I  built  a  barn  50  feet  long,  and  40  feet 
wide  lengthwise  in  the  south-west  corner  of  the  lot. 
The  side  walls  of  the  barn  are  20  feet  high.  Its  roof 
is  comb-shaped  and  rises  15  feet,  at  the  ridge.     This 


74  ARITHMETIC  BY  PRACTICE 

roof  projects  1  foot  at  the  eaves  and  gables.  A  fence 
six  boards  high  is  put  around  the  portion  of  the  lot  not 
taken  care  of  by  the  barn.  The  posts  are  10  feet  apart. 
In  neither  case  is  the  barn  used  as  a  post. 

1.  What  will  it  cost  to  sod  the  portion  of  the  lot  not 
covered  by  the  barn  at  12  cents  per  square  yard? 

2.  What  is  the  distance  from  the  north-east  corner 
of  the  barn  to  the  north-east  corner  of  the  lot? 

3.  How  many  board  feet  of  lumber  in  the  posts  if 
they  are  8  feet  long,  and  3  inches  square? 

4.  What  will  the  boards  for  the  fence  cost  at  90  cents 
per  hundred? 

5.  What  is  the  length  of  the  rafters? 

6.  How  much  siding  will  the  barn  require  including 
the  gables? 

7.  What  will  the  shingles  cost  at  $3.50  per  thousand, 
if  they  are  4  inches  wide,  and  are  placed  4^  inches  to 
the  weather?     (A  double  row  to  start  with.) 

8.  How  much  space  is  there  in  the  loft  if  its  floor  is 
3  feet  below  the  top  of  the  side  walls? 

9.  What  is  the  distance  from  the  top  of  the  siding 
of  the  north-east  corner  of  the  barn  to  the  north-east 
corner  of  the  lot? 


XII 

A  square  prism  has  for  the  sides  of  its  base  12  feet 
and  its  altitude  25  feet. 

1.  What  is  the  lateral  surface? 

2.  What  is  the  entire  surface? 


PROBLEMS  IN  MEASUREMENT  AND  MENSURATION  75 

3.  What  is  its  volume? 

4.  What  is  the  lateral  surface  of  a  pyramid  having 
the  same  dimensions? 

5.  What  is  the  entire  surface  of  the  pyramid? 

6.  What  is  its  volume? 


XIII 

The  radius  of  the  base  of  a  cylinder  is  8  feet,  and  its 
altitude  is  20  feet. 

1.  What  is  the  circumference  of  the  base? 

2.  What  is  the  convex  surface? 

3.  What  is  the  area  of  the  base? 

4.  What  is  the  entire  surface? 

5.  What  is  the  volume? 

6.  What  is  the  convex  surface  of  a  cone  with  the 
same  dimensions? 

7.  What  is  the  entire  surface? 

8.  What  is  the  volume? 


XIV 

I  wish  to  make  a  cistern  8  feet  in  diameter  and  10  feet 
deep  when  completed. 

1.  Not  making  any  allowance  for  cement,  what  will 
it  cost  to  excavate  the  cistern  at  75  cents  per  load? 

2.  What  will  it  cost  to  cement  the  bottom  and  wall 
at  25  cents  per  square  yard? 

3.  What  are  the  contents  of  the  cistern  in  gallons? 
In  barrels? 


76  ARITHMETIC  BY  PRACTICE 

4.  What  is  the  length  of  the  longest  stick  that  can 
be  placed  in  the  cistern? 

5.  What  would  be  the  contents  in  gallons  of  a 
conical  cistern  with  the  same  dimensions? 

XV 

I  wish  to  build  a  cylindrical  cistern  with  cemented 
bottom  and  wall.  It  is  to  be  8  feet  in  diameter  and  16 
feet  deep  when  completed. 

1.  What  will  it  cost  to  excavate  the  dirt  at  50  cents 
per  cubic  yard,  if  the  cement  at  the  bottom  is  made 
6  inches  thick,  and  the  wall  4  inches  thick? 

2.  What  is  the  cost  of  cementing  the  bottom  at 
75  cents  per  square  yard? 

3.  What  is  the  cost  of  cementing  the  wall  at  90 
cents,  per  square  yard? 

4.  What  is  the  capacity  of  the  cistern  in  gallons? 
In  barrels? 

5.  What  is  the  length  of  the  longest  stick  that  can 
be  placed  in  the  cistern? 

6.  What  will  be  the  total  cost  of  the  cistern? 

XVI 

Mr.  Smith  desires  to  build  a  cellar  30  feet  long, 
25  feet  wide,  and  8  feet  deep,  inside  measurements. 

1.  If  the  walls  are  2  feet  thick,  what  is  the  cost  of 
excavation  at  55  cents  per  cubic  yard? 

2.  What  will  be  the  cost  of  the  bricks  at  $8  per 
thousand,  no  allowance  being  made  for  mortar? 


PROBLEMS  IN  MEASUREMENT  AND  MENSURATION  77 

3.  What  is  the  diagonal  of  the  floor?     Of  the  cellar? 

4.  How  many  bushels  of  wheat  could  be  placed  in  a 
bin  with  the  same  dimensions? 

5.  How  many  gallons  of  water  in  a  tank  of  the  same 
dimensions? 


XVII 

4  inches 


-5 

2y2  inches 

;^ 

n 

1 

Vainch 

;5; 
1                          E 

1  inch 

F 

J 

2 

2  inches 

H 

G 

This  drawing  represents  a  plot  of  ground.     The  scale 
is  40  rods  to  the  inch. 

1.  What  is  the  perimeter  in  rods?    In  miles? 

2.  Extend  the  side  CD  until  it  will  intersect  AJ  as  at 
K.     What  is  the  area  of  ABCK? 

3.  Connect  E  and  I  by  a  straight  line.     What  is  the 
area  of  DEJK? 


78  ARITHMETIC  BY  PRACTICE 

4.  What  is  the  area  of  FGHI? 

5.  How  many  square  rods  in  the  whole  plot?    How 
many  acres? 

6.  The  area  of  FGHI  is  what  part  of  the  area  of  the 
whole  plot?    What  %? 

7.  What  is  the  distance  from  F  to  H? 

8.  Required  the  distance  from  D  to  I. 

9.  Required  the  distance  from  B  to  I. 

10.  The  length  of  FC  is  what  %  of  the  length  of  AG? 

11.  How  much  is  the  plot  of  ground  worth  at  $75 
per  acre? 

XVIII 

The  side  of  an  equilateral  triangle  is  18V3  inches. 

1.  What  is  the  area  of  the  triangle? 

2.  What  is  the  altitude  of  an  isosceles  triangle  having 
the  same  area,  and  whose  base  is  12  inches? 

3.  Required  the  altitude  of  a  rectangle  with  the 
same  area  and  a  base  of  20  inches. 

4.  Required  the  side  of  a  square  having  the  same 
area. 

5.  Required  the  base  of  a  rhombus  with  the  same 
area  and  whose  altitude  is  4  inches. 

6.  Required  the  altitude  of  a  trapezoid  having  the 
same  area,  and  whose  parallel  sides  are  respectively 
6  and  10  inches. 

7.  Required  the  radius  of  a  circle  having  the  same 
area. 

8.  Which  of  these  figures  has  the  shortest  perimeter? 
Which  has  the  longest  perimeter? 


PROBLEMS  IN  MEASUREMENT  AND  MENSURATION  79 

XIX 

A  certain  recitation  room  is  28  feet  long,  16  feet  wide 
and  10  feet  high. 

1.  Find  the  diagonal  of  the  floor. 

2.  What  is  the  diagonal  of  the  room? 

3.  What  is  the  lateral  surface  of  the  room?  What 
is  the  area  of  the  floor  and  ceiling? 

4.  What  is  the  volume  of  the  room  in  cubic  feet? 
In  cubic  yards? 

5.  The  room  has  three  windows  each  7  feet  by 
45  inches.     What  %  of  the  lateral  surface  is  glass? 

6.  There  are  two  blackboards,  each  4  feet  wide, 
extending  lengthwise  across  the  room.  What  is  the 
total  amount  of  blackboard  surface? 

7.  The  glass  surface  plus  the  board  surface  is  what 
per  cent  of  the  floor  surface? 

8.  How  many  gallons  of  water  will  a  tank  of  the 
same  dimensions  as  the  room  hold? 


XX 

In  a  certain  house  there  are  a  parlor,  a  sitting  room^ 
a  dining  room,  a  kitchen,  and  three  bedrooms. 

1.  The  dimensions  of  the  parlor  are  14  feet  by  12  feet 
by  10  feet.  What  will  it  cost  to  cover  the  floor  with  a 
carpet  |  of  a  yard  wide  at  $1.75  per  yard,  laying  it  the 
more  economical  way? 

2.  What  will  it  cost  to  paper  the  waUs  and  ceiling 
with  paper  at  40  cents  per  roll  put  on,  allowing  for 


80  ARITHMETIC  BY  PRACTICE 

two  windows  each  6  feet  by  45  inches  and  two  doors 
each  8  feet  by  3  feet? 

3.  The  dimensions  of  the  sitting  room  are  16  feet 
by  14  feet  by  12  feet.  Required  the  cost  of  carpeting 
it  with  carpet  f  of  a  yard  wide  at  $1.60  per  yard,  laying 
it  the  more  economical  way. 

4.  Required  the  cost  of  papering  the  walls  and  ceiling 
with  paper  at  35  cents  per  roll  put  on,  allowing  for 
3  windows  each  6  feet  by  4  feet  and  2  doors  each  8  feet 
by  39  inches. 

5.  The  dining  room  is  15  feet  by  12  feet  by  10  feet. 
Required  the  cost  of  carpeting  it  with  carpet  f  of  a 
yard  wide  at  $1.50  per  yard,  laying  it  the  more  economi- 
cal way. 

6.  The  dining  room  has  2  windows  each  6  feet  by 
40  inches  and  2  doors  each  8  feet  by  3  feet.  What 
will  it  cost  to  paper  the  room  with  paper  at  30  cents 
per  roll  put  on,  and  a  border  at  40  cents  per 
yard? 

7.  The  kitchen  is  12  feet  by  12  feet  by  10  feet. 
How  much  will  the  linoleum  cost  at  85  cents  per  yard 
in  two-yard  widths? 

8.  The  three  bedrooms  are  each  14  feet  by  12  feet 
by  10  feet.  What  will  the  matting  cost  for  the  three 
rooms  at  35  cents  per  yard? 

9.  Each  bedroom  has  two  windows  each  5  feet  by 
3  feet,  and  one  door  8  feet  by  3  feet.  What  will  the 
paper  cost  at  25  cents  per  roll  put  on,  and  a  border 
at  20  cents  per  yard? 

10.  What  is  the  total  cost  of  the  decorations  for  all 
the  rooms? 


I 


FOURTEEN  DAY  USE 

RETURN  TO  DESK  FROM  WHICH  BORROWED 

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T  n  91    1  rtH'n,  o^^K                                        General  Library 

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